Universitext

Algebraic Topology from a Homotopical Viewpoint

Authors: Aguilar, Marcelo, Gitler, Samuel, Prieto, Carlos

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About this Textbook

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.

Reviews

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 find many examples, calculations, and also a number of exercises. … The book has two appendices, … references consisting of 83 items and a long list of symbols. There are many remarks and comments making the orientation of the reader in the field of algebraic topology easier … ." (EMS, June, 2004)

"The modus operandi of algebraic topology is to associate algebraic invariants, such as groups or rings, to a topological space in such a way that equivalent spaces exhibit isomorphic invariants; here, ‘equivalent’ may be chosen to fit the geometry of the problem. In this book, ‘equivalent’ means homotopy equivalent … . For its clarity and directness, a welcome addition to advanced mathematics collections. Upper-division undergraduates through faculty." (J. McCleary, CHOICE, December, 2002)

"The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory … . The basic concepts of homotopy theory … are used to construct singular homology and cohomology, as well as K-theory. … Throughout the text many other fundamental concepts are introduced … ." (L’Enseignement Mathematique, Vol. 48 (3-4), 2002)

“The book of Aguilar, Gitler and Prieto gives an interesting new approach for a first course in algebraic topology. … What is also very interesting is the fact that the book contains a detailed presentation of some deep results of algebraic topology not usually covered by a first book in algebraic topology … . The text is carefully well written. … the student in algebraic topology will find in the book a lot of interesting well-exposed material.” (Yves Félix, Bulletin of the Belgian Mathematical Society, 2007)


Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-0-387-22489-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-0-387-95450-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $79.99
price for USA in USD
  • ISBN 978-1-4419-3005-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Topology from a Homotopical Viewpoint
Authors
Translated by
Sontz, S.B.
Series Title
Universitext
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-22489-3
DOI
10.1007/b97586
Hardcover ISBN
978-0-387-95450-9
Softcover ISBN
978-1-4419-3005-7
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XXIX, 479
Additional Information
Original Spanish edition published by McGraw-Hill Interamericana Editores, 1998
Topics