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• catalog abstract "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.".
• catalog contributor b12678600.
• catalog contributor b12678601.
• catalog contributor b12678602.
• catalog created "c2002.".
• catalog date "2002".
• catalog date "c2002.".
• catalog dateCopyrighted "c2002.".
• catalog description "Includes bibliographical references (p. 457-462) and index.".
• catalog description "Introduction -- Basic Concepts and Notation -- 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 -- References -- Index -- Glossary.".
• catalog description "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.".
• catalog extent "xxix, 478 p. :".
• catalog identifier "0387954503 (alk. paper)".
• catalog isPartOf "Universitext".
• catalog issued "2002".
• catalog issued "c2002.".
• catalog language "eng".
• catalog publisher "New York : Springer,".
• catalog subject "514/.2 21".
• catalog subject "Algebraic topology.".
• catalog subject "Homotopy theory.".
• catalog subject "Mathematics.".
• catalog subject "QA612 .A37 2002".
• catalog tableOfContents "Introduction -- Basic Concepts and Notation -- 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 -- References -- Index -- Glossary.".
• catalog title "Algebraic topology from a homotopical viewpoint / Marcelo Aguilar, Samuel Gitler, Carlos Prieto.".
• catalog type "text".