Topology and Geometry

Graduate Texts in Mathematics #139

by Glen E. Bredon

This book is intended as a textbook for a first-year graduate course on algebraic topology, with a strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. It covers most of the topics all topologists will want students to see, including surfaces, Lie groups, and fibre bundle theory.

With a thoroughly modern point of view, it is the first truly new textbook in topology since Spanier, almost 25 years ago. Although the book is comprehensive, there is no attempt made to present the material in excessive generality, except where generality improves the efficiency and clarity of the presentation.
--back cover

Genres: Mathematics, Geometry, Science, Textbooks

557 pages, Hardcover

First published January 1, 1993

Reviews

[Woflmao · Rating 4 out of 5]

There is no such thing as a good book on topology. If we accept this axiom, then Bredon does a decent job presenting the subject. The book begins with an introduction of general topology (open sets, continuous functions etc. up to topological groups) which is very good. The second part is on differential topology, and then the remainder of the book covers algebraic topology (homotopy and (co)homology), and the coverage is quite extensive. When someone writes a book of 500+ pages, it can be expected that at some points in the process they tire and it shows in the book; there is a certain inconsistency in the quality of the presentation and the level of detail. Unfortunately, sometimes very important concepts are submerged in these "lazy" chapters with sketchy explanations, and it is hard to follow the path once you stumble for the first time. The optional chapters indicated with a * are a hit and miss, often just long chunks of text with sketchy explanations that require additional literature to understand. To put it in perspective, comparable books (e.g. Hatcher's Algebraic Topology) do not do a better job here.

[Tanay]

Recommended by Claus Diem

[Stevenglinert · Rating 2 out of 5]

Just not a great textbook.