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.
Edited by:
Haynes Miller
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions:
Height: 254mm,
Width: 178mm,
Weight: 1.827kg
ISBN: 9781032917382
ISBN 10: 1032917385
Series: CRC Press/Chapman and Hall Handbooks in Mathematics Series
Pages: 990
Publication Date: 14 October 2024
Audience:
Professional and scholarly
,
Undergraduate
Format: Paperback
Publisher's Status: Active
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 Grothendieck–Teichmüller groups 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 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 MIT's highest teaching honor, the Margaret MacVicar Fellowship.
