**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

1999; 118 pp; Softcover

MSC: Primary 55; Secondary 57

**Print ISBN: 978-0-8218-1046-0**

Product Code: MMONO/183

Product Code: MMONO/183

List Price: $33.00

AMS Member Price: $26.40

MAA Member Price: $29.70

**Electronic ISBN: 978-1-4704-4597-3
Product Code: MMONO/183.E**

List Price: $31.00

AMS Member Price: $24.80

MAA Member Price: $27.90

# Algebraic Topology: An Intuitive Approach

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*Hajime Sato*

The single most difficult thing one faces when one begins to learn a new branch
of mathematics is to get a feel for the mathematical sense of the subject. The
purpose of this book is to help the aspiring reader acquire this essential
common sense about algebraic topology in a short period of time. To this end,
Sato leads the reader through simple but meaningful examples in concrete
terms. Moreover, results are not discussed in their greatest possible
generality, but in terms of the simplest and most essential cases.

In response to suggestions from readers of the original edition of this book,
Sato has added an appendix of useful definitions and results on sets, general
topology, groups and such. He has also provided references.

Topics covered include fundamental notions such as homeomorphisms, homotopy
equivalence, fundamental groups and higher homotopy groups, homology and
cohomology, fiber bundles, spectral sequences and characteristic
classes. Objects and examples considered in the text include the torus, the
Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector
bundles.

#### Readership

Graduate students and research mathematicians in algebraic topology.

#### Reviews & Endorsements

... Sato's book is a gem, and I am happy to recommend it in very enthusiastic terms.

-- MAA Reviews

This is an uncommon book with an interesting idea behind it, which is given in its title: to give an intuitive approach to algebraic topology. Instead of stating theorems in full generality or proving them rigorously with all technical details (or proving them at all), the author rather tries to make the reader familiar with "the idea" of the central notions of algebraic topology.

-- Zentralblatt MATH

A nice supplement for a topology course.

-- American Mathematical Monthly

The present book is an interesting, perhaps radical, survey of current algebraic topology. For a student who finds topology to be a forest of details, this text offers a chance to get an overview of the whole field.

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## Algebraic Topology: An Intuitive Approach

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xi12
- Preface to the English translation xiii14
- Objectives xv16
- Homeomorphisms and homotopy equivalences 120
- Topological spaces and cell complexes 928
- Homotopy 1736
- Homology 2746
- Homology groups of cell complexes 3958
- Cohomology 5574
- The Universal coefficient theorem 6180
- Fiber bundles and vector bundles 6988
- Spectral sequences 81100
- A view from current mathematics 99118
- Appendix 105124
- Answers to exercises 111130
- Recommended Reading 115134
- Index 117136
- Back Cover Back Cover1141