Handbook of Homotopy Theory by Haynes Miller (English) Hardcover Book

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The Handbook of Homotopy established the state-of-the-art research on this emerging topic in topology. The list of topics and contributors is impressive. The topics cover a broad swath, and the contributors will do an outstanding job. Students particularly will findthis book to be an entree to an active field of study.

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher 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.

Author Biography

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.

Table of Contents

Preface Gregory Arone and Michael Ching1 Goodwillie calculus David Ayala and John Francis2 A factorization homology primer Anthony Bahri, Martin Bendersky, and Frederick R. Cohen3 Polyhedral products and features of their homotopy theoryPaul Balmer4 A guide to tensor-triangular classification Tobias Barthel and Agnes Beaudry5 Chromatic structures in stable homotopy theory Mark Behrens6 Topological modular and automorphic forms Julia E. Bergner7 A survey of models for (1,n)-categories Gunnar Carlsson8 Persistent homology and applied homotopy theory Natalia Castellana9 Algebraic models in the homotopy theory of classifying spaces Ralph L. Cohen10 Floer homotopy theory, revisited Benoit Fresse11 Little discs operads, graph complexes and Grothendieck–TeichmüllergroupsSoren Galatius and Oscar Randal-Williams12 Moduli spaces of manifolds: a user's guide13 An introduction to higher categorical algebra Moritz Groth14 A short course on 1-categories Lars Hesselholt and Thomas Nikolaus15 Topological cyclic homology Gijs Heuts16 Lie algebra models for unstable homotopy theory Michael A. Hill17 Equivariant stable homotopy theory Daniel C. Isaksen and Paul Arne Ostvar18 Motivic stable homotopy groups Tyler Lawson19 En-spectra and Dyer-Lashof operations Wolfgang Luck20 Assembly maps Nathaniel Stapleton21 Lubin-Tate theory, character theory, and power operations Kirsten Wickelgren and Ben William22 Unstable motivic homotopy theory Index

Details ISBN0815369700 Publisher Taylor & Francis Inc Series CRC Press/Chapman and Hall Handbooks in Mathematics Series ISBN-10 0815369700 ISBN-13 9780815369707 Format Hardcover Imprint CRC Press Inc Place of Publication Bosa Roca Country of Publication United States Year 2019 DEWEY 514.24 Language English Illustrations 3 Tables, black and white; 20 Illustrations, black and white Publication Date 2019-12-23 AU Release Date 2019-12-23 NZ Release Date 2019-12-23 US Release Date 2019-12-23 UK Release Date 2019-12-23 Author Haynes Miller Edited by Haynes Miller Pages 990 Audience Tertiary & Higher Education We've got this

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