Handbook of Homotopy Theory 1st Edition by Haynes Miller ISBN 9780815369707 0815369700

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Product details:

ISBN 10:   0815369700

ISBN 13: 9780815369707

Author:  Haynes Miller 

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 Poincaré 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 ¥ -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.

Table of contents: 

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 (∞, 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 Grothendieck-Teichmüller groups

12. Moduli spaces of manifolds: a user’s guide

13. An introduction to higher categorical algebra

14. A short course on ∞-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

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Tags: Haynes Miller, Handbook, Homotopy Theory