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The Resource Introduction to homotopy theory, Martin Arkowitz

Introduction to homotopy theory, Martin Arkowitz

Label
Introduction to homotopy theory
Title
Introduction to homotopy theory
Statement of responsibility
Martin Arkowitz
Creator
Subject
Genre
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1935-
http://library.link/vocab/creatorName
Arkowitz, M.
Illustrations
illustrations
Index
index present
Literary form
non fiction
Nature of contents
bibliography
Series statement
Universitext,
http://library.link/vocab/subjectName
Homotopy theory
Label
Introduction to homotopy theory, Martin Arkowitz
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
1. Basic Homotopy -- 1.1. Introduction -- 1.2. Spaces, Maps, Products, and Wedges -- 1.3. Homotopy I -- 1.4. Homotopy II -- 1.5. CW Complexes -- 1.6. Why Study Homotopy Theory? -- Exercises -- 2. H-Spaces and Co-H-Spaces -- 2.1. Introduction -- 2.2. H-Spaces and Co-H-Spaces -- 2.3. Loop Spaces and Suspensions -- 2.4. Homotopy Groups I -- 2.5. Moore Spaces and Eilenberg-Mac Lane Spaces -- 2.6. Eckmann-Hilton Duality I -- Exercises -- 3. Cofibrations and Fibrations -- 3.1. Introduction -- 3.2. Cofibrations -- 3.3. Fibrations -- 3.4. Examples of Fiber Bundles -- 3.5. Replacing a Map by a Cofiber or Fiber Map -- Exercises -- 4. Exact Sequences -- 4.1. Introduction -- 4.2. The Coexact and Exact Sequence of a Map -- 4.3. Actions and Coactions -- 4.4. Operations -- 4.5. Homotopy Groups II -- Exercises -- 5. Applications of Exactness -- 5.1. Introduction -- 5.2. Universal Coefficient Theorems -- 5.3. Homotopical Cohomology Groups -- 5.4. Applications to Fiber and Cofiber Sequences -- 5.5. The Operation of the Fundamental Group -- 5.6. Calculation of Homotopy Groups -- Exercises -- 6. Homotopy Pushouts and Pullbacks -- 6.1. Introduction -- 6.2. Homotopy Pushouts and Pullbacks I -- 6.3. Homotopy Pushouts and Pullbacks II -- 6.4. Theorems of Serre, Hurewicz, and Blakers-Massey -- 6.5. Eckmann-Hilton Duality II -- Exercises -- 7. Homotopy and Homology Decompositions -- 7.1. Introduction -- 7.2. Homotopy Decompositions of Spaces -- 7.3. Homology Decompositions of Spaces -- 7.4. Homotopy and Homology Decompositions of Maps -- Exercises -- 8. Homotopy Sets -- 8.1. Introduction -- 8.2. The Set [X, Y] -- 8.3. Category -- 8.4. Loop and Group Structure in [X, Y] -- Exercises -- 9. Obstruction Theory -- 9.1. Introduction -- 9.2. Obstructions Using Homotopy Decompositions -- 9.3. Lifts and Extensions -- 9.4. Obstruction Miscellany -- Exercises
Control code
ocn749913070
Dimensions
24 cm
Extent
xiii, 344 p.
Isbn
9781441973283
Lccn
2011933473
Other physical details
ill.
System control number
(OCoLC)749913070
Label
Introduction to homotopy theory, Martin Arkowitz
Publication
Bibliography note
Includes bibliographical references and index
Contents
1. Basic Homotopy -- 1.1. Introduction -- 1.2. Spaces, Maps, Products, and Wedges -- 1.3. Homotopy I -- 1.4. Homotopy II -- 1.5. CW Complexes -- 1.6. Why Study Homotopy Theory? -- Exercises -- 2. H-Spaces and Co-H-Spaces -- 2.1. Introduction -- 2.2. H-Spaces and Co-H-Spaces -- 2.3. Loop Spaces and Suspensions -- 2.4. Homotopy Groups I -- 2.5. Moore Spaces and Eilenberg-Mac Lane Spaces -- 2.6. Eckmann-Hilton Duality I -- Exercises -- 3. Cofibrations and Fibrations -- 3.1. Introduction -- 3.2. Cofibrations -- 3.3. Fibrations -- 3.4. Examples of Fiber Bundles -- 3.5. Replacing a Map by a Cofiber or Fiber Map -- Exercises -- 4. Exact Sequences -- 4.1. Introduction -- 4.2. The Coexact and Exact Sequence of a Map -- 4.3. Actions and Coactions -- 4.4. Operations -- 4.5. Homotopy Groups II -- Exercises -- 5. Applications of Exactness -- 5.1. Introduction -- 5.2. Universal Coefficient Theorems -- 5.3. Homotopical Cohomology Groups -- 5.4. Applications to Fiber and Cofiber Sequences -- 5.5. The Operation of the Fundamental Group -- 5.6. Calculation of Homotopy Groups -- Exercises -- 6. Homotopy Pushouts and Pullbacks -- 6.1. Introduction -- 6.2. Homotopy Pushouts and Pullbacks I -- 6.3. Homotopy Pushouts and Pullbacks II -- 6.4. Theorems of Serre, Hurewicz, and Blakers-Massey -- 6.5. Eckmann-Hilton Duality II -- Exercises -- 7. Homotopy and Homology Decompositions -- 7.1. Introduction -- 7.2. Homotopy Decompositions of Spaces -- 7.3. Homology Decompositions of Spaces -- 7.4. Homotopy and Homology Decompositions of Maps -- Exercises -- 8. Homotopy Sets -- 8.1. Introduction -- 8.2. The Set [X, Y] -- 8.3. Category -- 8.4. Loop and Group Structure in [X, Y] -- Exercises -- 9. Obstruction Theory -- 9.1. Introduction -- 9.2. Obstructions Using Homotopy Decompositions -- 9.3. Lifts and Extensions -- 9.4. Obstruction Miscellany -- Exercises
Control code
ocn749913070
Dimensions
24 cm
Extent
xiii, 344 p.
Isbn
9781441973283
Lccn
2011933473
Other physical details
ill.
System control number
(OCoLC)749913070

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