Handbook of Homotopy Theory  book cover
1st Edition

Handbook of Homotopy Theory

Edited By

Haynes Miller

ISBN 9780815369707
Published December 23, 2019 by Chapman and Hall/CRC
990 Pages 20 B/W Illustrations

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Book Description

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


Gregory Arone and Michael Ching

1 Goodwillie calculus

David Ayala and John Francis

2 A factorization homology primer

Anthony Bahri, Martin Bendersky, and Frederick R. Cohen

3 Polyhedral products and features of their homotopy theory

Paul Balmer

4 A guide to tensor-triangular classification

Tobias Barthel and Agnes Beaudry

5 Chromatic structures in stable homotopy theory

Mark Behrens

6 Topological modular and automorphic forms

Julia E. Bergner

7 A survey of models for (1,n)-categories

Gunnar Carlsson

8 Persistent homology and applied homotopy theory

Natalia Castellana

9 Algebraic models in the homotopy theory of classifying spaces

Ralph L. Cohen

10 Floer homotopy theory, revisited

Benoit Fresse

11 Little discs operads, graph complexes and Grothendieck–Teichmüller


Soren Galatius and Oscar Randal-Williams

12 Moduli spaces of manifolds: a user’s guide

13 An introduction to higher categorical algebra

Moritz Groth

14 A short course on 1-categories

Lars Hesselholt and Thomas Nikolaus

15 Topological cyclic homology

Gijs Heuts

16 Lie algebra models for unstable homotopy theory

Michael A. Hill

17 Equivariant stable homotopy theory

Daniel C. Isaksen and Paul Arne Ostvar

18 Motivic stable homotopy groups

Tyler Lawson

19 En-spectra and Dyer-Lashof operations

Wolfgang Luck

20 Assembly maps

Nathaniel Stapleton

21 Lubin-Tate theory, character theory, and power operations

Kirsten Wickelgren and Ben William

22 Unstable motivic homotopy theory



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Haynes Miller is Professor of Mathematics at the Massachusetts Institute of Technology. Past managing editor of the Bulletin of the American Mathematical Society and author of some sixty mathematics articles, he has directed the PhD work of 27 students during his tenure at MIT. His visionary work in university-level education was recognized by the award of MIT’s highest teaching honor, the Margaret MacVicar Fellowship.