Handbook of Homotopy Theory

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. Contents Preface 1 Goodwillie calculus 2 A factorization homology primer 3 Polyhedral products and features of their homotopy theory 4 A guide to tensor-triangular classification 5 Chromatic structures in stable homotopy theory 6 Topological modular and automorphic forms 7 A survey of models for (∞, n)-categories 8 Persistent homology and applied homotopy theory 9 Algebraic models in the homotopy theory of classifying spaces 10 Floer homotopy theory, revisited 11 Little discs operads, graph complexes and Grothendieck–Teichmüller groups 12 Moduli spaces of manifolds: a user’s guide 13 An introduction to higher categorical algebra 14 A short course on ∞-categories 15 Topological cyclic homology 16 Lie algebra models for unstable homotopy theory 17 Equivariant stable homotopy theory 18 Motivic stable homotopy groups 19 En-spectra and Dyer-Lashof operations 20 Assembly maps 21 Lubin-Tate theory, character theory, and power operations 22 Unstable motivic homotopy theory Index