Algebraic Topology from a Homotopical Viewpoint

  • Marcelo Aguilar
  • Samuel Gitler
  • Carlos Prieto

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxix
  2. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 1-7
  3. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 9-57
  4. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 59-88
  5. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 89-147
  6. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 149-188
  7. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 189-226
  8. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 227-258
  9. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 259-287
  10. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 289-307
  11. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 309-329
  12. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 331-382
  13. Marcelo Aguilar, Samuel Gitler, Carlos Prieto
    Pages 383-419
  14. Back Matter
    Pages 421-479

About this book

Introduction

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.

Keywords

Adams operation Brown representability Category theory Characteristic class Homotopy group algebraic invariant cofibration cohomology group fibrations function space group theory homological algebra homotopy extension homotopy theory point set topology

Authors and affiliations

  • Marcelo Aguilar
    • 1
  • Samuel Gitler
    • 2
  • Carlos Prieto
    • 1
  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMéxico, DFMéxico
  2. 2.Departamento de MatemáticasCentro de Investigación y de Estudios AvanzadosMéxico, DFMéxico

Bibliographic information

  • DOI https://doi.org/10.1007/b97586
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3005-7
  • Online ISBN 978-0-387-22489-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book