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.
Preface
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 GrothendieckTeichmüller
groups
Soren Galatius and Oscar Randal-Williams
12 Moduli spaces of manifolds: a users 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
Index
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 MITs highest teaching honor, the Margaret MacVicar Fellowship.
Lisainfo e-raamatute kohta