Handbook of Homotopy Theory

<p>The <b><i>Handbook of Homotopy Theory</i></b> 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.</p><p>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. </p> <p>Preface </p><p>Gregory Arone and Michael Ching</p><p>1 Goodwillie calculus </p><p>David Ayala and John Francis</p><p>2 A factorization homology primer </p><p>Anthony Bahri, Martin Bendersky, and Frederick R. Cohen</p><p>3 Polyhedral products and features of their homotopy theory</p><p>Paul Balmer</p><p>4 A guide to tensor-triangular classification </p><p>Tobias Barthel and Agnes Beaudry</p><p>5 Chromatic structures in stable homotopy theory </p><p>Mark Behrens</p><p>6 Topological modular and automorphic forms </p><p>Julia E. Bergner</p><p>7 A survey of models for (1<i>,n</i>)-categories </p><p>Gunnar Carlsson</p><p>8 Persistent homology and applied homotopy theory </p><p>Natalia Castellana</p><p>9 Algebraic models in the homotopy theory of classifying spaces </p><p>Ralph L. Cohen</p><p>10 Floer homotopy theory, revisited </p><p>Benoit Fresse</p><p>11 Little discs operads, graph complexes and Grothendieck–Teichmüller</p><p>groups</p><p>Soren Galatius and Oscar Randal-Williams</p><p><strong>12 Moduli spaces of manifolds: a user’s guide</strong></p><p>13 An introduction to higher categorical algebra </p><p>Moritz Groth</p><p>14 A short course on 1-categories </p><p>Lars Hesselholt and Thomas Nikolaus</p><p>15 Topological cyclic homology </p><p>Gijs Heuts</p><p>16 Lie algebra models for unstable homotopy theory </p><p>Michael A. Hill</p><p>17 Equivariant stable homotopy theory </p><p>Daniel C. Isaksen and Paul Arne Ostvar</p><p>18 Motivic stable homotopy groups </p><p>Tyler Lawson</p><p>19 <i>En</i>-spectra and Dyer-Lashof operations </p><p>Wolfgang Luck</p><p>20 Assembly maps </p><p>Nathaniel Stapleton</p><p>21 Lubin-Tate theory, character theory, and power operations </p><p>Kirsten Wickelgren and Ben William</p><p>22 Unstable motivic homotopy theory </p><p>Index </p>