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Handbook of Homotopy Theory

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

• Haynes Miller (ed.)

  Handbook of Homotopy Theory (table of contents)

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 $(\infty,n)$-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, $E_n$-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

    
    

Related entries

• Handbook of Algebraic Topology

category: reference