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Algebraic Topology

by

Algebraic Topology Cover

 

Synopses & Reviews

Publisher Comments:

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.

Synopsis:

Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes and other topics. Each chapter contains exercises and suggestions for further readi

Synopsis:

Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes, and other topics. Each chapter contains exercises and suggestions for further reading. 1980 corrected edition.

Table of Contents

CHAPTER 1 ALGEBRAIC AND TOPOLOGICAL PRELIMINARIES

1.1 Introduction

1.2 Set theory

1.3 Algebra

1.4 Analytic Topology

CHAPTER 2 HOMOTOPY AND SIMPLICIAL COMPLEXES

2.1 Introduction

2.2 The classification problem; homotopy

2.3 Simplicial complexes

2.4 Homotopy and homeomorphism of polyhedra

2.5 Subdivision and the Simplicial Approximation Theorem

  Exercises

  Notes on Chapter 2

CHAPTER 3 THE FUNDAMENTAL GROUP

3.1 Introduction

3.2 Definition and elementary properties of the fundamental group

3.3 Methods of calculation

3.4 Classification of triangulable 2-manifolds

  Exercises

  Notes on Chapter 3

CHAPTER 4 HOMOLOGY THEORY

4.1 Introduction

4.2 Homology groups

4.3 Methods of calculation: simplicial homology

4.4 Methods of calculation: exact sequences

4.5 "Homology groups with arbitrary coefficients, and the Lefschetz Fixed-Point Theorem"

  Exercises

  Notes on Chapter 4

CHAPTER 5 COHOMOLOGY AND DUALITY THEOREMS

5.1 Introduction

5.2 Definitions and calculation theorems

5.3 The Alexander-Poincaré Duality Theorem

5.4 Manifolds with boundary and the Lefschetz Duality Theorem

  Exercises

  Notes on Chapter 5

CHAPTER 6 GENERAL HOMOTOPY THEORY

6.1 Introduction

6.2 Some geometric constructions

6.3 Homotopy classes of maps

6.4 Exact sequences

6.5 Fibre and cofibre maps

  Exercises

  Notes on Chapter 6

CHAPTER 7 HOMOTOPY GROUPS AND CW-COMPLEXES

7.1 Introduction

7.2 Homotopy groups

7.3 CW-complexes

7.4 Homotopy groups of CW-complexes

7.5 The theorem of J. H. C. Whitehead and the Cellular Approximation Theorem

  Exercises

  Notes on Chapter 7

CHAPTER 8 HOMOLOGY AND COHOMOLOGY OF CW-COMPLEXES

8.1 Introduction

8.2 The Excision Theorem and cellular homology

8.3 The Hurewicz theorem

8.4 Cohomology and Eilenberg-MacLane spaces

8.5 Products

  Exercises

  Notes on Chapter 8

References

Index

Product Details

ISBN:
9780486691312
Author:
Maunder, C. R. F.
Publisher:
Dover Publications
Author:
Mathematics
Location:
Mineola, N.Y. :
Subject:
General
Subject:
Algebra
Subject:
Algebra - General
Subject:
Topology
Subject:
Algebraic topology
Subject:
Topology - General
Subject:
General Mathematics
Subject:
Mathematics - General
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19960631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
400
Dimensions:
8.5 x 5.38 in 0.94 lb

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Related Subjects

Metaphysics » General
Reference » Encyclopedias » General
Science and Mathematics » Materials Science » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Topology

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Product details 400 pages Dover Publications - English 9780486691312 Reviews:
"Synopsis" by , Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes and other topics. Each chapter contains exercises and suggestions for further readi
"Synopsis" by ,
Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes, and other topics. Each chapter contains exercises and suggestions for further reading. 1980 corrected edition.
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