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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. The presentation of the homotopy theory and the account of duality in homology manifolds make the text ideal for a course on either homotopy or homology theory.
The idea of algebraic topology is to translate problems in topology into problems in algebra with the hope that they have a better chance of solution. The translation process is usually carried out by means of the homology or homotopy groups of a topological space. Much of the book is therefore concerned with the construction of these algebraic invariants, and with applications to topological problems, such as the classification of surfaces and duality theorems for manifolds. Other important topics covered are homotopy theory, CW-complexes and the co-homology groups associated with a general Ω-spectrum.
Dr. Maunder has provided many examples and exercises as an aid, and the notes and references at the end of each chapter trace the historical development of the subject and also point the way to more advanced results.
"Throughout the text the style of writing is first class. The author has given much attention to detail, yet ensures that the reader knows where he is going. An excellent book." — Bulletin of the Institute of Mathematics and Its Applications.

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. Includes exercises. Bibliography. 1980 corrected edition.

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:

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.

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:
Maunder, C. R. F.
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
Copyright:
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 1 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
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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. Includes exercises. Bibliography. 1980 corrected edition.

"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 , 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.
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