This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS
Topology and Geometry (Graduate Texts in Mathematics)
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Editorial Reviews
Review
G.E. Bredon Topology and Geometry "An interesting and original graduate text in topology and geometry. The topics covered include . . . general topology, smooth manifolds, homology and homotopy groups, duality, cohomology and products . . . a good lecturer can use this text to create a fine course at the appropriate level . . . There are various innovative things, which are accessible but not traditionally covered. A beginning graduate student can use this text to learn a great deal of mathematics."—MATHEMATICAL REVIEWS
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Most Helpful Customer Reviews
17 of 19 people found the following review helpful:
5.0 out of 5 stars
The Graduate Sudent's Topology Bible,
By
This review is from: Topology and Geometry (Graduate Texts in Mathematics) (Hardcover)
If you want to learn topology, this book is the place. Though this text can require some maturity, the range of topics and the clarity of exposition are outstanding. My only complaint is that an additional appendix covering the basics of category theory would have been quite useful. Bredon not infrequently uses the language of category theory (though always in a non-essential way). Since this text is aimed at 1st year graduate students, I think the tacit assumption that the student has already encountered these topics is not justified. That such a minor point is my chief complaint speaks volumes of my esteem for this text.
14 of 17 people found the following review helpful:
3.0 out of 5 stars
a different perspective,
By chicken head cut off "mcscientist" (Gainesville/Orsay France) - See all my reviews
This review is from: Topology and Geometry (Graduate Texts in Mathematics) (Hardcover)
While I agree with reviewers generally that this is a good book, i should warn that bredon isnt for the faint of heart. He makes use of simple language from category theory, doesnt always completely introduce his discussions (see for example the chapter on the tangent bundle where tangent bundle is never defined), and some other things that are nuisances to the newcomer.
I do think this is a good modern readable textbook, but for the student who has a solid foundation in mathematics. I didnt find it as accessable as other topology books, say Hatcher or Lee's books (but lee's are not as complete).
19 of 25 people found the following review helpful:
5.0 out of 5 stars
My secret weapon in topology,
By curtken@ksu.edu (Manhattan, KS) - See all my reviews
This review is from: Topology and Geometry (Graduate Texts in Mathematics) (Hardcover)
Today I told someone that Bredon's "Topology and Geometry" book was my secret weapon. I say this because it has mostly everything a grad student in topology needs to know in order to be fluent in the subject. I bought it not because I was taking a class from it--I got it because I saw it at the library and realized that this is the 'end all' topology book for me and that I will not need to buy all those 'other' books in topology anymore. I will warn you though--some of the proofs are terse, so you have to be somewhat 'mathematically mature'. It is definately harder than Munkres' "Topology: A first course" (the red book). But it goes beyond the point set crap that gets (in my opinion) too much airtime. I wish I would have taken a class under this book.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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bounded finite type, pointed category, affine simplex, homotopy extension property, singular simplices, cochain level, unreduced suspension, terminal singularities, constant homotopy, disk bundle, homotopy axiom, singular simplex, identifying antipodal points, suspension isomorphism, homotopy inverse, finite subcomplex, universal net, chain map, mapping cylinder, lifting problem, chain homotopic, cobordism classes, paracompact spaces, free homotopy, attaching map Key Phrases - Capitalized Phrases (CAPs): (learn more)
Universal Coefficient Theorem, Differentiable Manifolds, Hurewicz Theorem, Rham's Theorem, Sard's Theorem, Hopf's Theorem, Tubular Neighborhood Theorem, The Generalized Jordan Curve Theorem, Use Corollary, Use Problem, Bootstrap Lemma, Rham Theorem, Differential Forms, Maximality Principle, Stiefel Whitney, Euler's Formula, Moore-Smith Convergence, Thom Isomorphism Theorem, Thom-Pontryagin Theory New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
bounded finite type, pointed category, affine simplex, homotopy extension property, singular simplices, cochain level, unreduced suspension, terminal singularities, constant homotopy, disk bundle, homotopy axiom, singular simplex, identifying antipodal points, suspension isomorphism, homotopy inverse, finite subcomplex, universal net, chain map, mapping cylinder, lifting problem, chain homotopic, cobordism classes, paracompact spaces, free homotopy, attaching map Key Phrases - Capitalized Phrases (CAPs): (learn more)
Universal Coefficient Theorem, Differentiable Manifolds, Hurewicz Theorem, Rham's Theorem, Sard's Theorem, Hopf's Theorem, Tubular Neighborhood Theorem, The Generalized Jordan Curve Theorem, Use Corollary, Use Problem, Bootstrap Lemma, Rham Theorem, Differential Forms, Maximality Principle, Stiefel Whitney, Euler's Formula, Moore-Smith Convergence, Thom Isomorphism Theorem, Thom-Pontryagin Theory New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
See all 100 books citing this book
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), Back Matter (2), and Back Matter (3)
- General Topology (Graduate Texts in Mathematics) by John L. Kelley in Front Matter, and Back Matter
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- An Introduction to Algebraic Topology (Graduate Texts in Mathematics) by Joseph J. Rotman in Back Matter (1), and Back Matter (2)
- The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) (v. 106) by Joseph H. Silverman in Back Matter (1), and Back Matter (2)
See all 100 books this book cites
- Introduction to Topological Manifolds (Graduate Texts in Mathematics) by John M. Lee in Front Matter, and Back Matter
- Sheaf Theory (Graduate Texts in Mathematics) by Glen E. Bredon in Back Matter (1), and Back Matter (2)
- Lectures on Discrete Geometry by Jiri Matousek in Back Matter (1), and Back Matter (2)
- Lectures on Discrete Geometry (Graduate Texts in Mathematics) by Matousek, Jiri in Back Matter (1), and Back Matter (2)
- Introduction to Topological Manifolds (Graduate Texts in Mathematics) by John M. Lee in Front Matter, and Back Matter
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