Differential Forms in Algebraic Topology
Dive into the fascinating world of Differential Forms in Algebraic Topology, where the elegant interplay between geometry and algebra unfolds. Authors Raoul Bott and Loring W. Tu guide readers through complex concepts with clarity and insight, revealing the beauty behind these mathematical structures. With a perfect blend of theory and application, this book illuminates how differential forms serve as powerful tools in various contexts of topology. Each chapter invites readers to engage with profound ideas that challenge and inspire. Are you ready to embark on a journey that transforms your understanding of the mathematical universe?
By Raoul Bott, Loring W. Tu
Published: 1995
""In the intricate dance of differential forms, we uncover the hidden symmetries of space, revealing that the beauty of mathematics lies not just in answers, but in the questions we dare to explore.""
Start Listening
What Readers Say About This Book
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
The Mike & Casey Show
Dive into captivating book discussions with our expert hosts
Key Points from Differential Forms in Algebraic Topology
About the Authors
Raoul Bott
Raoul Bott was a renowned mathematician, celebrated for his profound contributions to topology and algebraic geometry. His notable works include 'The Bott Periodicity Theorem,' 'The Intersection Homology,' and significant contributions to the theory of characteristic classes. Often recognized for his clear and insightful writing style, Bott's works blend rigorous mathematical concepts with intuitive explanations, making complex ideas accessible. His collaborations and lectures have inspired generations of mathematicians.
Loring W. Tu
Loring W. Tu is a prominent author known for his expertise in historical fiction and compelling narratives. His notable works include "The Chronicles of the Forgotten" trilogy and "Echoes of the Past," both celebrated for their rich character development and intricate plots. Tu's writing style is characterized by vivid imagery and meticulous research, bringing historical settings to life while exploring timeless themes of love, loss, and resilience. Through his storytelling, he invites readers to reflect on the complexities of the human experience.
Book Details
Key information about the book.
- Authors
- Raoul Bott, Loring W. Tu
- Published
- May 1995
- Publisher
- Springer
- ISBN
- 0387906134
- Language
- English
- Pages
- 334
- Genres
- Non-FictionScientific Discoveries
Purchase Options
Buy on Amazon
Buy via BookShopSupport local bookstores: BookShop gives a portion of each sale to independent bookshops!
Similar books you might like →
Crises of Democracy
Adam Przeworski
I Hate Your Guts
Jim Norton
Dig Safe
Stuart Dischell
Lie Algebras In Particle Physics
Howard Georgi
Out of My Later Years
Albert Einstein
Modern Geometry — Methods and Applications
B.A. Dubrovin, A.T. Fomenko, S.P. Novikov
Differential Topology
Victor Guillemin, Alan Pollack
Lab Girl
Hope Jahren
The Undocumented Americans
Karla Cornejo Villavicencio
A Confederacy of Dunces
John Kennedy Toole
Simulation and Its Discontents
Sherry Turkle
The Moth Snowstorm
Michael McCarthy
A Liberated Mind
Steven Hayes
The Poisonwood Bible
Barbara Kingsolver
Infinite in All Directions
Freeman J. Dyson
Whiteshift
Eric Kaufmann
Unshakeable
Tony Robbins, Peter Mallouk
Free Will
Sam Harris
Just Keep Buying
Nick Maggiulli
Assembling Life
David W. Deamer
Top Dog
Po Bronson, Ashley Merryman
The Lowland
Jhumpa Lahiri
American Prison
Shane Bauer
Mother Night
Kurt Vonnegut
Dreams of a Final Theory
Steven Weinberg
59 Seconds
Richard Wiseman
The Wedding Date
Jasmine Guillory
Every Little Step
Bobby Brown, Nick Chiles
Take your reading experience to the next level
Download our mobile app to enjoy your favorite books on the go. Get access to exclusive features, offline listening, and personalized recommendations.
Book Collections you might like →
Chris Dixon's Book Recommendations
Chris Dixon is a notable venture capitalist and technology entrepreneur, best known for his influential role as a general partner at Andreessen Horowitz, where he leads investments in cryptocurrency and blockchain technology. Before joining the firm, Dixon co-founded two startups: SiteAdvisor, a web security company acquired by McAfee, and Hunch, a recommendation engine acquired by eBay. In addition to his investment career, Dixon is a prolific writer and thought leader on technology and innovation, contributing insightful essays and articles to various platforms such as his personal blog and Medium. His writings often explore the future of technology, the internet, and the impact of blockchain, making significant contributions to contemporary tech literature. Dixon's work has earned him recognition as a visionary in both the tech and literary worlds.
View Collection
Haruki Murakami's Book Recommendations
Haruki Murakami is an internationally acclaimed Japanese author known for his surreal, magical realist style, blending elements of reality with the fantastical in his novels. His works, such as "Norwegian Wood," "Kafka on the Shore," and "1Q84," have captivated readers with their dreamlike narratives, introspective characters, and deep exploration of existential themes. Murakami's unique voice often explores loneliness, isolation, and the complexities of human nature. His use of metaphors and symbolism has earned him a dedicated global following, and his books have been translated into dozens of languages. A reclusive figure, Murakami avoids public appearances and prefers to let his work speak for itself, although he occasionally writes essays and non-fiction on topics such as running, jazz, and literature. Murakami has been a strong contender for the Nobel Prize in Literature for years, and his influence on contemporary fiction is undeniable. Beyond his writing, Murakami is also an avid marathon runner and music enthusiast, elements that often appear in his narratives.
View Collection
Hamilton Morris's Book Recommendations
Hamilton Morris is an American journalist, documentarian, and chemist renowned for his extensive work on psychoactive substances. He is best known for his series "Hamilton's Pharmacopeia," which explores the history, chemistry, and cultural impact of various psychoactive drugs. Morris has contributed significantly to the literature on ethnopharmacology, providing in-depth research and firsthand accounts that have enriched public understanding of these substances. His writings and documentaries have been featured in prominent publications such as Vice, Harper's Magazine, and National Geographic. An advocate for scientific rigor and cultural sensitivity, Hamilton Morris continues to influence both the scientific community and popular discourse on psychoactive substances.
View Collection
Dave Chappelle's Book Recommendations
Dave Chappelle is an American comedian, actor, and writer, widely regarded as one of the greatest stand-up comedians of all time. He gained fame with Chappelle’s Show, a sketch comedy series that offered sharp social commentary on race, politics, and culture. After stepping away from the show at the height of its popularity, Chappelle made a triumphant return to stand-up and has since released several acclaimed specials on Netflix. Known for his fearless humor and insightful critiques of society, Chappelle’s influence on comedy is profound. He continues to perform and speak on issues of race, identity, and justice.
View Collection
Andrew Lokenauth's Book Recommendations
Andrew Lokenauth is a distinguished author and financial expert known for his insightful contributions to personal finance and investment literature. With a career spanning over a decade, he has written extensively on topics such as wealth management, financial planning, and market analysis. Lokenauth's works are celebrated for their clarity and practical advice, making complex financial concepts accessible to a broad audience. He has been featured in numerous financial publications and has established himself as a trusted voice in the industry. Beyond his writing, Lokenauth is also a sought-after speaker, sharing his expertise at various seminars and workshops.
View Collection
Barack Obama's Book Recommendations
Barack Obama is the 44th President of the United States, serving from 2009 to 2017. As the first African American president, Obama’s leadership marked a historic moment in American history. His administration focused on healthcare reform, economic recovery from the Great Recession, and environmental policies. He is best known for the Affordable Care Act, as well as his efforts to expand civil rights and restore diplomatic relations with Cuba. Since leaving office, Obama has continued to engage in public life through his foundation, focusing on leadership development, civic engagement, and global issues.
View Collection
Drew Houston's Book Recommendations
Drew Houston is an accomplished American entrepreneur best known for co-founding Dropbox, a widely-used cloud storage service, in 2007. As the CEO, he has led the company to serve millions of users worldwide and become a key player in the tech industry. Although not primarily known for literature, Houston has shared his entrepreneurial insights and experiences through various interviews and public speaking engagements, offering valuable lessons to aspiring business leaders. His work has significantly influenced the way people and organizations manage and share digital content. Houston's innovative vision continues to shape the future of cloud computing and digital collaboration.
View Collection
Ann Miura-Ko's Book Recommendations
Ann Miura-Ko is a distinguished venture capitalist and co-founding partner at Floodgate, a seed-stage investment firm known for backing transformative tech startups. While not primarily an author in the traditional sense, her thought leadership and influential writings on entrepreneurship and venture capital have shaped industry perspectives. She is a lecturer at Stanford University, where her insights into the intersection of technology and business are highly valued by students and peers alike. Ann is also a founding member of All Raise, an organization dedicated to increasing diversity in venture capital and entrepreneurship. Her contributions to literature primarily lie in her impactful essays and articles that guide and inspire the next generation of innovators.
View Collection
Andrew Chen's Book Recommendations
Andrew Chen is a venture capitalist, entrepreneur, and thought leader in growth marketing, currently serving as a general partner at Andreessen Horowitz. Chen is known for his expertise in network effects, viral growth strategies, and marketplace dynamics, making him a sought-after advisor for startups looking to scale. Prior to joining Andreessen Horowitz, he worked in leadership roles at Uber, helping to grow the ride-sharing platform’s user base and develop key growth strategies. Chen is also a prolific writer, sharing his insights on growth, technology, and startups through his popular blog and newsletter, which has attracted a loyal following in the tech community. His work has helped shape how many startups approach user acquisition, retention, and product-market fit. As a venture capitalist, Chen focuses on early-stage companies in the consumer internet, SaaS, and marketplace sectors, and he has been involved in funding and advising several successful startups. His insights on technology and growth continue to influence both founders and investors alike.
View Collection
Andrew Wilkinson's Book Recommendations
Andrew Wilkinson is a distinguished author and entrepreneur, best known for his insightful business writings and contributions to the tech industry. He co-founded MetaLab, a prominent design agency that has shaped the user experience of major platforms like Slack and Coinbase. Wilkinson's entrepreneurial journey and his publications provide valuable perspectives on startup culture, innovation, and leadership. His writing, often featured in leading business magazines and his personal blog, has garnered a wide readership for its practical advice and engaging storytelling. Andrew continues to influence both literature and the business world with his unique blend of creativity and strategic thinking.
View Collection
David Sinclair's Book Recommendations
David Sinclair is an Australian biologist and professor at Harvard Medical School, known for his pioneering research in the field of aging and longevity. Sinclair's work focuses on understanding the biological mechanisms that drive aging and developing interventions to slow or reverse the process. His bestselling book Lifespan: Why We Age – and Why We Don’t Have To explores the latest advancements in anti-aging science and offers insights into how humans might extend their healthspan. Sinclair's research has led to breakthroughs in areas such as sirtuins, NAD+ metabolism, and cellular reprogramming. He is also the co-founder of several biotech companies, including Sirtris Pharmaceuticals and Life Biosciences, dedicated to translating aging research into practical treatments. Sinclair is a vocal advocate for taking a proactive approach to aging, promoting lifestyle changes and emerging therapies to delay age-related diseases. His work has made him a leading figure in the longevity movement, influencing both scientific and public discourse on the future of health.
View Collection
Daniel Petre's Book Recommendations
Daniel Petre is a distinguished Australian entrepreneur, author, and philanthropist known for his impactful contributions to the business and literary worlds. He co-founded the venture capital firm AirTree Ventures, which has significantly influenced the technology startup ecosystem in Australia. Petre has authored several influential books on technology and leadership, including "The Clever Country?" and "Father Time," which explore themes of innovation and work-life balance. His writing often reflects his deep commitment to shaping a forward-thinking, inclusive society. Beyond his literary and business endeavors, Petre is also recognized for his substantial philanthropic efforts, particularly in education and healthcare.
View Collection
Jason Fried's Book Recommendations
Jason Fried is an influential entrepreneur and author best known as the co-founder and CEO of Basecamp, a project management and team collaboration software company. He has notably co-authored several best-selling books, including "Rework" and "Remote: Office Not Required," which challenge conventional business practices and advocate for more efficient, flexible work environments. Fried's clear, straightforward writing style has resonated with a wide audience, making complex business concepts accessible. His work has significantly contributed to the discourse on modern work culture and productivity. Fried continues to influence contemporary business thought through his writing and leadership at Basecamp.
View Collection
Elon Musk's Book Recommendations
Elon Musk is an influential entrepreneur and innovator known for founding and leading several groundbreaking companies, including Tesla, SpaceX, Neuralink, and The Boring Company. He has played a pivotal role in advancing electric vehicles, space exploration, and renewable energy. Musk's vision extends to colonizing Mars and reducing the risk of human extinction through space travel. In addition to his technological contributions, he has co-authored the book "Spacex: Making Commercial Spaceflight a Reality," providing insights into his ambitious projects and vision for the future. Musk's relentless pursuit of innovation continues to shape the trajectory of multiple industries.
View Collection
Bill Gates's Book Recommendations
Bill Gates, co-founder of Microsoft Corporation, is a pioneering figure in the tech industry, having played a key role in the personal computer revolution. His work at Microsoft, particularly the development of Windows, transformed software and computing globally. Beyond his technology contributions, Gates is also a prolific author, with notable works such as "The Road Ahead" and "Business @ the Speed of Thought," which offer insights into the future of technology and business. Additionally, his philanthropic efforts through the Bill & Melinda Gates Foundation have had a profound impact on global health, education, and poverty. Gates continues to influence both technology and literature with his forward-thinking perspectives and innovative ideas.
View Collection
Brian Cox's Book Recommendations
Brian Cox is a Scottish actor and director, best known for his roles in films like Braveheart and Adaptation, as well as for his portrayal of media mogul Logan Roy in the hit HBO series Succession. Cox is renowned for his commanding screen presence and his ability to convey complex, often morally ambiguous characters. He has had a distinguished career in both film and theater, earning numerous awards, including a Golden Globe for his performance in Succession. In addition to his acting work, Cox is a vocal advocate for arts education and has been involved in various charitable initiatives. His longevity and versatility have made him a respected and influential figure in the entertainment industry.
View Collection
Brian Armstrong's Book Recommendations
Brian Armstrong is a renowned entrepreneur and author best known for co-founding and leading Coinbase, a major cryptocurrency exchange. His literary contributions include insightful writings on the future of digital currencies and blockchain technology. Armstrong's work has been pivotal in demystifying complex financial systems for a broader audience. Beyond his business acumen, his thought leadership in publications and public speaking engagements has cemented his status as a key voice in the fintech revolution. His dedication to innovation continues to influence the trajectory of global financial systems.
View Collection
Seth Godin's Book Recommendations
Seth Godin is a prolific author and entrepreneur, renowned for his influential contributions to marketing and business thought leadership. He has written over 20 bestselling books, including "Purple Cow," "Linchpin," and "The Dip," which have revolutionized modern marketing strategies and inspired countless professionals. Godin's work emphasizes the importance of creativity, innovation, and the power of ideas in building successful enterprises. He is also the founder of altMBA, an online leadership and management workshop, and he consistently shares his insights through his popular daily blog. Godin's impact on the marketing world has earned him a spot in the Direct Marketing Hall of Fame.
View Collection
James Altucher's Book Recommendations
James Altucher is an American hedge fund manager, entrepreneur, author, and podcaster known for his candid and unconventional approach to success and self-improvement. He has authored over 20 books, including bestsellers like "Choose Yourself" and "Reinvent Yourself," which emphasize the importance of resilience and personal empowerment. Altucher is also a prolific blogger, sharing insights on various topics ranging from finance to mental health. His podcast, "The James Altucher Show," features in-depth interviews with a diverse array of influential figures, further cementing his reputation as a thought leader. Through his writing and media presence, Altucher has inspired millions to embrace failure as a stepping stone to success.
View Collection
Benedict Evans's Book Recommendations
Benedict Evans is a renowned technology analyst and commentator, acclaimed for his insightful analyses on technology trends and their societal impacts. With a background in venture capital and strategic consulting, Evans has become a prominent voice in the tech community through his thought-provoking essays and presentations. His work often explores the intersection of mobile technology, media, and internet platforms, offering a nuanced understanding of complex tech ecosystems. Evans is widely respected for his ability to distill intricate technological developments into accessible and compelling narratives. His contributions have significantly influenced industry leaders and informed public discourse on the future of technology.
View Collection
Bill Burr's Book Recommendations
Bill Burr is an American comedian, actor, and podcaster, known for his biting, no-nonsense style of humor that often tackles controversial topics with sharp wit. Burr has released several successful stand-up specials, including Paper Tiger and Walk Your Way Out, and is the co-creator of the animated sitcom F Is for Family. He also hosts the Monday Morning Podcast, where he shares his unfiltered thoughts on everything from current events to personal stories. Burr’s honest, raw comedic style has earned him a dedicated fanbase and has made him one of the most respected comedians in the industry.
View Collection
Frank Chimero's Book Recommendations
Frank Chimero is a renowned designer, illustrator, and author best known for his influential book "The Shape of Design," which explores the philosophy and practice of design. His work emphasizes the intersection of creativity and human experience, earning him a respected place in both the design and literary communities. Chimero has contributed essays and lectures that have inspired a new generation of thinkers in the creative industries. He has also been recognized for his ability to distill complex ideas into accessible, thought-provoking content. Beyond his writing, Chimero's design projects and illustrations have been featured in numerous prestigious publications and exhibitions.
View Collection
Michael Mauboussin's Book Recommendations
Michael Mauboussin is a renowned investment strategist and author, known for his influential work in the fields of finance and behavioral economics. He has authored several acclaimed books, including "More Than You Know: Finding Financial Wisdom in Unconventional Places" and "The Success Equation: Untangling Skill and Luck in Business, Sports, and Investing." Mauboussin serves as Head of Consilient Research at Counterpoint Global, a division of Morgan Stanley Investment Management. His insights into decision-making, market behavior, and investment strategies have made significant contributions to both academic literature and practical applications in finance. Additionally, Mauboussin is a frequent lecturer and has taught at esteemed institutions like Columbia Business School.
View Collection“"In the intricate dance of differential forms, we uncover the hidden symmetries of space, revealing that the beauty of mathematics lies not just in answers, but in the questions we dare to explore."”
Differential Forms in Algebraic Topology
By Raoul Bott, Loring W. Tu
Frequently Asked Questions
Explore Our Catalogue
Discover a world of knowledge through our extensive collection of book summaries.