- 982 pages
- English
- ePUB (mobile friendly)
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Handbook of Homotopy Theory
About This Book
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri PoincarĆ© and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of Ā„ -categories.
The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
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Table of contents
- Cover
- Half Title
- Series Page
- Title Page
- Copyright Page
- Contents
- Preface
- 1. Goodwillie calculus
- 2. A factorization homology primer
- 3. Polyhedral products and features of their homotopy theory
- 4. A guide to tensor-triangular classification
- 5. Chromatic structures in stable homotopy theory
- 6. Topological modular and automorphic forms
- 7. A survey of models for (ā,n)-categories
- 8. Persistent homology and applied homotopy theory
- 9. Algebraic models in the homotopy theory of classifying spaces
- 10. Floer homotopy theory, revisited
- 11. Little discs operads, graph complexes and GrothendieckāTeichmĆ¼ller groups
- 12. Moduli spaces of manifolds: a userās guide
- 13. An introduction to higher categorical algebra
- 14. A short course on ā-categories
- 15. Topological cyclic homology
- 16. Lie algebra models for unstable homotopy theory
- 17. Equivariant stable homotopy theory
- 18. Motivic stable homotopy groups
- 19. En-spectra and Dyer-Lashof operations
- 20. Assembly maps
- 21. Lubin-Tate theory, character theory, and power operations
- 22. Unstable motivic homotopy theory
- Index