Cubical Homotopy Theory

✍ Scribed by Brian A. Munson, Ismar Volić

• Publisher: Cambridge University Press
• Year: 2015
• Tongue: English
• Leaves: 647
• Series: New Mathematical Monographs 25
• Category: Library

✦ Synopsis

Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological spaces with an emphasis on cubical diagrams. The book contains 300 examples and provides detailed explanations of many fundamental results. Part I focuses on foundational material on homotopy theory, viewed through the lens of cubical diagrams: fibrations and cofibrations, homotopy pullbacks and pushouts, and the Blakers–Massey Theorem. Part II includes a brief example-driven introduction to categories, limits and colimits, an accessible account of homotopy limits and colimits of diagrams of spaces, and a treatment of cosimplicial spaces. The book finishes with applications to some exciting new topics that use cubical diagrams: an overview of two versions of calculus of functors and an account of recent developments in the study of the topology of spaces of knots.

✦ Table of Contents

Preface
Part I. Cubical Diagrams: 1. Preliminaries
2. 1-cubes: homotopy fibers and cofibers
3. 2-cubes: homotopy pullbacks and pushouts
4. 2-cubes: the Blakers-Massey Theorems
5. n-cubes: generalized homotopy pullbacks and pushouts
6. The Blakers-Massey Theorems for n-cubes
Part II. Generalizations, Related Topics, and Applications: 7. Some category theory
8. Homotopy limits and colimits of diagrams of spaces
9. Cosimplicial spaces
10. Applications
Appendix
References
Index.

✦ Subjects

Homotopy theory;Cube;Algebraic topology