Ebook: Algebraic Topology from a Homotopical Viewpoint

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.

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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 Aut?noma de M?xico, and Samuel Gitler is a member of El Colegio Nacional and professor at the Centro de Investigaci?n y Estudios Avanzados del IPN.

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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 Aut?noma de M?xico, and Samuel Gitler is a member of El Colegio Nacional and professor at the Centro de Investigaci?n y Estudios Avanzados del IPN.
Content:
Front Matter....Pages i-xxix
Function Spaces....Pages 1-7
Connectedness and Algebraic Invariants....Pages 9-57
Homotopy groups....Pages 59-88
Homotopy Extension and Lifting Properties....Pages 89-147
CW-Complexes and Homology....Pages 149-188
Homotopy Properties of CW-Complexes....Pages 189-226
Cohomology Groups and Related Topics....Pages 227-258
Vector Bundles....Pages 259-287
K-Theory....Pages 289-307
Adams Operations and Applications....Pages 309-329
Relations Between Cohomology and Vector Bundles....Pages 331-382
Cohomology Theories and Brown Representability....Pages 383-419
Back Matter....Pages 421-478

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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 Aut?noma de M?xico, and Samuel Gitler is a member of El Colegio Nacional and professor at the Centro de Investigaci?n y Estudios Avanzados del IPN.
Content:
Front Matter....Pages i-xxix
Function Spaces....Pages 1-7
Connectedness and Algebraic Invariants....Pages 9-57
Homotopy groups....Pages 59-88
Homotopy Extension and Lifting Properties....Pages 89-147
CW-Complexes and Homology....Pages 149-188
Homotopy Properties of CW-Complexes....Pages 189-226
Cohomology Groups and Related Topics....Pages 227-258
Vector Bundles....Pages 259-287
K-Theory....Pages 289-307
Adams Operations and Applications....Pages 309-329
Relations Between Cohomology and Vector Bundles....Pages 331-382
Cohomology Theories and Brown Representability....Pages 383-419
Back Matter....Pages 421-478
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