Graduate Texts in Mathematics

Algebraic Topology

A First Course

Authors: Fulton, William

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About this Textbook

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

Table of contents (24 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4612-4180-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-0-387-94327-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Topology
Book Subtitle
A First Course
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
153
Copyright
1995
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, Inc.
eBook ISBN
978-1-4612-4180-5
DOI
10.1007/978-1-4612-4180-5
Softcover ISBN
978-0-387-94327-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XVIII, 430
Number of Illustrations and Tables
13 b/w illustrations
Topics