Handbook of Homotopy Theory (eBook, PDF)

Redaktion: Miller, Haynes

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 990
• Erscheinungstermin: 23. Januar 2020
• Englisch
• ISBN-13: 9781351251617
• Artikelnr.: 58558371

Inhaltsangabe

Preface



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

groups



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

Index