Brian A. Munson

Cubical Homotopy Theory (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 6. Oktober 2015
• Englisch
• ISBN-13: 9781316348932
• Artikelnr.: 52989294

Autorenporträt

Brian A. Munson is an Assistant Professor of Mathematics at the US Naval Academy. He has held postdoctoral and visiting positions at Stanford University, Harvard University, and Wellesley College, Massachusetts. His research area is algebraic topology, and his work spans topics such as embedding theory, knot theory, and homotopy theory.

Inhaltsangabe

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.