Cubical homotopy theory
Author(s)
Bibliographic Information
Cubical homotopy theory
（New mathematical monographs, 25）
Cambridge University Press, 2015
- : hardback
Available at 10 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackMUN||8||1200033912186
-
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: hardback/M 9282080383027
Note
Includes bibliographical references (p. 600-612) and index
Description and Table of Contents
Description
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.
by "Nielsen BookData"