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Handbook of Homotopy Theory

Edited by: Haynes Miller

Print publication date:  December  2019
Online publication date:  December  2019

Print ISBN: 9780815369707
eBook ISBN: 9781351251624
Adobe ISBN:

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Book 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 Â¥ -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.

Table of contents

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