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Algebraic Topology : A First Course - William Fulton

Algebraic Topology

A First Course

Paperback

Published: 5th September 1997
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To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol- ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel- opment of the subject. What would we like a student to know after a first course in to- pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under- standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind- ing numbers and degrees of mappings, fixed-point theorems; appli- cations such as the Jordan curve theorem, invariance of domain; in- dices of vector fields and Euler characteristics; fundamental groups

W. Fulton

Algebraic Topology

A First Course

"Fulton has done genuine service for the mathematical community by writing a text on algebraic topology which is genuinely different from the existing texts. Each time a text such as this is published we more truly have a real choice when we pick a book for a course or for self-study. The author, who is an expert in algebraic geometry, has given us his own personal idiosyncratic vision of how the subject should be developed."AMERICAN MATHEMATICAL MONTHLY

Preface
Calculus in the Plane
Winding Numbers
Cohomology and Homology, I
Vector Fields
Cohomology and Homology, II
Covering Spaces and Fundamental Groups, I
Covering Spaces and Fundamental Groups, II
Cohomology and Homology, III
Topology of Surfaces
Riemann Surfaces
Higher Dimensions
Appendices
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387943275
ISBN-10: 0387943277
Series: Graduate Texts in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 430
Published: 5th September 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 2.3
Weight (kg): 0.68