Algebraic Topology from a Homotopical Viewpoint

Marcelo Aguilar, Samuel Gitler, Carlos Prieto

478 pages, parution le 25/07/2002

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Résumé

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.

Contents

Function Spaces.
Connectedness and Algebraic Invariants.
Homotopy Groups.
Homotopy Extension 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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Marcelo Aguilar, Samuel Gitler, Carlos Prieto
Parution	25/07/2002
Nb. de pages	478
Format	16 x 24,5
Couverture	Relié
Poids	830g
Intérieur	Noir et Blanc
EAN13	9780387954509
ISBN13	978-0-387-95450-9