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Introduction to Homotopy Theory

By Martin Arkowitz

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This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.

Full Description

  • ISBN13: 978-1-4419-7328-3
  • 357 Pages
  • Publication Date: July 25, 2011
  • Available eBook Formats: PDF
  • eBook Price: $74.95
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Full Description
This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. It is assumed that the reader has had some exposure to the rudiments of homology theory and fundamental group theory. These topics are discussed in the appendices. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.
Table of Contents

Table of Contents

  1. 1 Basic Homotopy.
  2. 2 H
  3. Spaces and Co
  4. H
  5. Spaces.
  6. 3 Cofibrations and Fibrations.
  7. 4 Exact Sequences.
  8. 5 Applications of Exactness.
  9. 6 Homotopy Pushouts and Pullbacks.
  10. 7 Homotopy and Homology Decompositions.
  11. 8 Homotopy Sets.
  12. 9 Obstruction Theory.
  13. A Point
  14. Set Topology.
  15. B The Fundamental Group.
  16. C Homology and Cohomology.
  17. D Homotopy Groups and the n
  18. Sphere.
  19. E Homotopy Pushouts and Pullbacks.
  20. F Categories and Functors.
  21. Hints to Some of the Exercises.
  22. References.
  23. Index.
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