1st Edition

Handbook of Homotopy Theory

Edited By Haynes Miller Copyright 2020
    990 Pages 20 B/W Illustrations
    by Chapman & Hall

    990 Pages 20 B/W Illustrations
    by Chapman & Hall

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    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.


    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




    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.