nLab Handbook of Homotopy Theory

This page compiles material related to the book collection:

on homotopy theory/algebraic topology, including higher algebra and higher category theory.


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.


  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 December 19, 2020 at 11:52:45. See the history of this page for a list of all contributions to it.