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Algebraic Topology from a Homotopical Viewpoint

Algebraic Topology from a Homotopical Viewpoint
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Field name Details
Dewey Class 514
Title Algebraic Topology from a Homotopical Viewpoint ([EBook] /) / by Marcelo Aguilar, Samuel Gitler, Carlos Prieto.
Author Aguilar, Marcelo
Added Personal Name Gitler, Samuel author.
Prieto, Carlos author.
Other name(s) SpringerLink (Online service)
Publication New York, NY : : Springer New York : : Imprint: Springer, , 2002.
Physical Details XXIX, 479 p. : online resource.
Series Universitext 0172-5939
ISBN 9780387224893
Summary Note 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.:
Contents note Function Spaces -- Connectedness and Algebraic Invariants -- Homotopy groups -- Homotopy Extension and Lifting Properties -- CW-Complexes and 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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