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Algebraic topology from a homotopical viewpoint

Author: M A Aguilar; Samuel Gitler; C Prieto
Publisher: New York : Springer, ©2002.
Series: Universitext.
Edition/Format:   eBook : EnglishView all editions and formats
Database:WorldCat
Summary:
"The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications in algebraic geometry as understood by Lawson and Voevodsky. This method allows the authors to cover the material more efficiently than the more common method using homological algebra. The basic concepts of homotopy theory, such as fibrations and cofibrations, are used to  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Aguilar, M.A. (Marcelo A.).
Algebraic topology from a homotopical viewpoint.
New York : Springer, ©2002
(DLC) 2002019556
Material Type: Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: M A Aguilar; Samuel Gitler; C Prieto
ISBN: 0387224890 9780387224893 0585472246 9780585472249
OCLC Number: 559536745
Description: 1 online resource (xxix, 478 pages) : illustrations.
Contents: Cover --
Preface --
Table of Contents --
Introduction --
Basic Concepts and Notation --
1. Function Spaces --
2. Connectedness and Algebraic Invariants --
3. Homotopy groups --
4. Homotopy Extension and Lifting Properties --
5. CW-Complexes and Homology --
6. Homotopy Properties of CW-Complexes --
7. Cohomology Groups and Related Topics --
8. Vector Bundles --
9. K-Theory --
10. Adams Operations and Applications --
11. Relations Between Cohomology and Vector Bundles --
12. Cohomology Theories and Brown Representability --
Appendix A --
Proof of the Dold-Thom Theorem --
Appendix B --
Proof of the Bott Periodicity Theorem --
References --
Symbols.
Series Title: Universitext.
Responsibility: Marcelo Aguilar, Samuel Gitler, Carlos Prieto.

Abstract:

Presents introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This book is suitable for any student who knows some topology, providing a  Read more...

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From the reviews: "This is a basic course on algebraic topology and ... it is excellently written and composed and can be strongly recommended to anybody wishing to learn the field. The reader can Read more...

 
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schema:reviewBody""The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications in algebraic geometry as understood by Lawson and Voevodsky. This method allows the authors to cover the material more efficiently than the more common method using homological algebra. The basic concepts of homotopy theory, such as fibrations and cofibrations, are used to construct singular homology and cohomology, as well as K-theory. Throughout the text many other fundamental concepts are introduced, including the construction of the characteristic classes of vector bundles. Although functors appear constantly throughout the book, no previous knowledge about category theory is expected from the reader. This book is intended for advanced undergraduate and graduate students with a basic background in point set topology as well as group theory and can be used in a two-semester course."--Jacket."
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