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Handbook of Homotopy Theory

A book published on December 23, 2019 by Chapman and Hall/CRC (ISBN 9780815369707), 982 pages.

on homotopy theory, including higher algebra and higher category theory.

Terminology

The editor, Haynes Miller, comments in the introduction on the choice of title:

This volume may be regarded as a successor to the “Handbook of Algebraic Topology,” edited by Ioan James and published a quarter of a century ago. In calling it the “Handbook of Homotopy Theory,” I am recognizing that the discipline has expanded and deepened, and traditional questions of topology, as classically understood, are now only one of many distinct mathematical disciplines in which it has had a profound impact and which serve as sources of motivation for research directions within homotopy theory proper.

Contributions

  1. Gregory Arone, Michael Ching, Goodwillie Calculus, (arXiv:1902.00803)


    on Goodwillie calculus


  2. David Ayala, John Francis, A factorization homology primer, (arXiv: 1903.10961)


    on factorization homology


  3. Anthony Bahri, Martin Bendersky, and Fred Cohen, Polyhedral products and features of their homotopy theory, (arXiv:1903.04114)


  4. Paul Balmer, A guide to tensor-triangular classification, (arXiv:1912.08963)


    on tensor triangulated categories


  5. Tobias Barthel and Agnès Beaudry, Chromatic structures in stable homotopy theory, (arXiv:1901.09004)


    on chromatic homotopy theory


  6. Mark Behrens, Topological modular and automorphic forms (arXiv:1901.07990)


    on topological modular forms


  7. Julia Bergner, A survey of models for (,n)(\infty,n)-categories (arXiv:1810.10052)


    on (infinity,n)-categories


  8. Gunnar Carlsson, Persistent homology and applied homotopy theory (arXiv:2004.00738)


    on persistent homology in topological data analysis


  9. Natàlia Castellana, Algebraic models in the homotopy theory of classifying spaces


    on classifying spaces


  10. Ralph Cohen, Floer homotopy theory, revisited (arXiv:1901.08694)


  11. Benoit Fresse, Little discs operads, graph complexes and Grothendieck–Teichmüller groups, (arXiv:1811.12536)


    on little disc operads, graph complexes and the Grothendieck-Teichmueller group


  12. Søren Galatius, Oscar Randal-Williams, Moduli spaces of manifolds: a user’s guide, (arXiv:1811.08151)


    on cobordism categories


  13. David Gepner, An Introduction to Higher Categorical Algebra, (arXiv:1907.02904)


    on higher algebra


  14. Moritz Groth, A short course on \infty-categories, (arXiv:1007.2925)


    on (infinity,1)-categories


  15. Lars Hesselholt, Thomas Nikolaus, Topological cyclic homology, (arXiv:1905.08984)


    on topological cyclic homology


  16. Gijs Heuts, Lie algebra models for unstable homotopy theory, (arXiv:1907.13055)


  17. Michael Hill, Equivariant stable homotopy theory


    on equivariant stable homotopy theory


  18. Daniel Isaksen, Paul Arne Østvær, Motivic stable homotopy groups, (arXiv:1811.05729)


    on motivic homotopy theory


  19. Tyler Lawson, E nE_n-ring spectra and Dyer-Lashof operations, (arXiv:2002.03889, differently-formatted author pdf)


    on E_n-ring spectra and power operations


  20. Wolfgang Lueck, Assembly Maps, (arXiv:1805.00226)


    on assembly maps


  21. Nathaniel Stapleton, Lubin-Tate theory, character theory, and power operations, (arXiv:1810.12339)


    on Lubin-Tate theory and power operations


  22. Kirsten Wickelgren, Ben Williams, Unstable Motivic Homotopy Theory, (arXiv: 1902.08857)


    on motivic homotopy theory


category: reference

Last revised on April 5, 2020 at 10:16:52. See the history of this page for a list of all contributions to it.