Algebraic Topology from a Homotopical Viewpoint / Edition 1 by Marcelo Aguilar, Samuel Gitler, Carlos Prieto | | 9781441930057 | Paperback | Barnes & Noble
Algebraic Topology from a Homotopical Viewpoint / Edition 1

Algebraic Topology from a Homotopical Viewpoint / Edition 1

by Marcelo Aguilar, Samuel Gitler, Carlos Prieto
     
 

ISBN-10: 1441930051

ISBN-13: 9781441930057

Pub. Date: 12/14/2011

Publisher: Springer New York

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,

Overview

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 text, no knowledge about category theory is expected from the reader. This book is intended for advanced undergraduates and graduate students with a basic knowledge of point set topology as well as group theory and can be used in a two semester course.
Marcelo Aguilar and Carlos Prieto are Professors at the Instituto de Matemticas, Universidad Nacional Autónoma de México, and Samuel Gitler is a member of El Colegio Nacional and professor at the Centro de Investigación y Estudios Avanzados del IPN.

Product Details

ISBN-13:
9781441930057
Publisher:
Springer New York
Publication date:
12/14/2011
Series:
Universitext Series
Edition description:
Softcover reprint of hardcover 1st ed. 2002
Pages:
479
Product dimensions:
6.14(w) x 9.21(h) x 1.03(d)

Related Subjects

Table of Contents

* Introduction
• Basic Concepts and Notation
• Function Spaces
• Connectedness and Algebraic Invariants
• Homotopy Groups
• Homotopy Extentsion and Lifting Properties
• CW-Complexes Homology
• Homotopy Properties of CW-Complexes
• Cohomology Groups and Related Topics
• Vector Bundles
• K-Theory
• Adams Operations and Applications
• Relations Between Cohomology and Vector Bundles
• Cohomology Theories and Brown Representability
• Appendix A: Proof of the Dold-Thom Theorem
• Appendix B: Proof of the Bott Periodicity Theorem
• References
• Index
• Glossary *

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