nLab Peter May (changes)

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J. Peter May is a homotopy theorist at the University of Chicago, inventor of operads as a technique for studying infinite loop spaces and spectra.

• Peter May’s webpage.

• Peter May: Wikipedia entry.

Peter May’s work makes extensive use of enriched- and model-category theory as power tools in algebraic topology/homotopy theory, notably in discussion of highly structured spectra in MMSS00‘s Model categories of diagram spectra (for exposition see Introduction to Stable homotopy theory -- 1-2), or in the discussion of genuine equivariant spectra or K-theory of permutative categories, etc.. While he has co-edited a book collection on higher category theory (Baez-May 10) and eventually had high praise (May 16) for 2-category theory as a tool in algebraic topology/higher algebra, he has vocally warned against seeing abstract (∞,1)-category theory as a replacement for concrete realizations in model category-theory (P. May, MO comment Dec 2013).

Selected writings

On algebraic topology

• Peter May, A concise course in algebraic topology

• Peter May, Kate Ponto, More concise algebraic topology

On simplicial objects in algebraic topology (simplicial homotopy theory):

• Peter May, Simplicial objects in algebraic topology, University of Chicago Press 1967 (ISBN:9780226511818, djvu, pdf)

On infinite loop spaces:

• Peter May, The geometry of iterated loop spaces, 1972 (pdf)

• Peter May, Infinite loop space theory, Bull. Amer. Math. Soc. Volume 83, Number 4 (1977), 456-494. (Euclid)

  Infinite loop space theory revisited (pdf)

On equivariant algebraic K-theory:

• Zbigniew Fiedorowicz, Henning Hauschild, Peter May, Equivariant algebraic K-theory, in: Algebraic K-Theory, Lecture Notes in Mathematics 967, Springer (1982) 23-80 [[doi:10.1007/BFb0061898](https://doi.org/10.1007/BFb0061898), pdf]

On $E_\infty$-spaces and $E_\infty$-ring sectra:

• L. Gaunce Lewis, Peter May, Mark Steinberger (with contributions by J.E. McClure), Equivariant stable homotopy theory, Springer Lecture Notes in Mathematics 1213 (1986) [[pdf](http://www.math.uchicago.edu/~may/BOOKS/equi.pdf), doi:10.1007/BFb0075778]

On equivariant cohomology and equivariant homotopy theory:

• Peter May et al., Equivariant homotopy and cohomology theory, CBMS Regional Conference Series in Mathematics Volume: 91; 1996 (ISBN:978-0-8218-0319-6, pdf, pdf)

On highly structured spectra:

• Michael Mandell, Peter May, Stefan Schwede, Brooke Shipley, Model categories of diagram spectra, Proceedings of the London Mathematical Society Volume 82, Issue 2, 2000 (pdf, doi:10.1112/S0024611501012692)

On $H_\infty$-ring spectra:

• Robert Bruner, Peter May, James McClure, Mark Steinberger, $H_\infty$-Ring Spectra and their Applications, Lecture Notes in Mathematics 1176, Springer (1986) [[doi:10.1007/BFb0075405](https://link.springer.com/book/10.1007/BFb0075405), pdf]

On equivariant bundles:

• Richard Lashof, Peter May, Generalized equivariant bundles, Bull. Soc. Math. Belg. Sér. A 38, 265-271, 1986 (pdf, pdf)

On classifying spaces/universal principal bundles for equivariant principal bundles:

• Peter May, Some remarks on equivariant bundles and classifying spaces, Théorie de l’homotopie, Astérisque, no. 191 (1990), 15 p. (numdam:AST_1990__191__239_0)

• Bertrand Guillou, Peter May, Mona Merling Categorical models for equivariant classifying spaces, Algebr. Geom. Topol. 17 (2017) 2565-2602 (arXiv:1201.5178, doi:10.2140/agt.2017.17.2565)

On equivariant bundles with abelian structure group:

• Richard Lashof, Peter May, Graeme Segal, Equivariant bundles with abelian structural group, Contemporary Mathematics, Volume 19, 1983 (doi:10.1090/conm/019, pdf, pdf)

On higher algebra (brave new algebra) in stable homotopy theory, i.e. on ring spectra, module spectra etc.:

• Anthony Elmendorf, Igor Kriz, Michael Mandell, Peter May, Rings, modules and algebras in stable homotopy theory, Mathematical Surveys and Monographs Volume 47, AMS 1997 (ISBN:978-0-8218-4303-1, pdf)

On module spectra:

• Peter May, Equivariant and non-equivariant module spectra, Journal of Pure and Applied Algebra Volume 127, Issue 1, 1 May 1998, Pages 83–97 (pdf)

On operads and motives:

• Igor Kriz, Peter May, Operads, algebras, modules and motives, Astérisque 233, Société Mathématique de France (1995).

On equivariant stable homotopy theory:

• L. Gaunce Lewis, Peter May, and Mark Steinberger (with contributions by J.E. McClure), Equivariant stable homotopy theory, Springer Lecture Notes in Mathematics Vol. 1213. 1986 (pdf, doi:10.1007/BFb0075778)

On equivariant complex oriented cohomology theory:

• Steven Costenoble, Peter May, Stefan Waner, Equivariant orientation theory, Homology Homotopy Appl. Volume 3, Number 2 (2001), 265-339 (euclid:hha/1139840256)

On tensor triangulated categories and traces:

• Peter May, The Additivity of Traces in Triangulated Categories, Advances in Mathematics, Volume 163, Issue 1, 2001, Pages 34-73 (doi:10.1006/aima.2001.1995)

On the Picard infinity-group of equivariant stable homotopy theory and the notion of RO(G)-grading:

• Halvard Fausk, L. Gaunce Lewis, Peter May, The Picard group of equivariant stable homotopy theory, Advances in Mathematics Volume 163, Issue 1, 15 October 2001, Pages 17–33 (pdf)

On six operations and Wirthmüller contexts:

• Halvard Fausk, Po Hu, Peter May, Isomorphisms between left and right adjoints, Theory and Applications of Categories, 11 4 (2003) 107-131 [[tac:11-04](http://www.tac.mta.ca/tac/volumes/11/4/11-04abs.html), pdf]

On parametrized stable homotopy theory:

• Peter May, Johann Sigurdsson, Parametrized Homotopy Theory, Mathematical Surveys and Monographs, vol. 132, AMS 2006 (ISBN:978-0-8218-3922-5, arXiv:math/0411656, pdf)

On enriched model category theory:

• Bertrand Guillou, Peter May, Enriched model categories and presheaf categories, New York J. Math. 26 (2020) 37–9 (arXiv:1110.3567, , NYJM:2020/26-3)

On higher category theory:

• John Baez, Peter May (eds.), Towards Higher Categories, Springer 2010 (doi:10.1007/978-1-4419-1524-5)

Specifically on 2-category theory as a tool in spectral algebraic geometry, equivariant homotopy theory and infinite loop space-theory:

• Peter May, Input for derived algebraic geometry:equivariant multiplicativeinfinite loop space theory, Banff 2016 (pdf, pdf)

On equivariant homotopy theory and Elmendorf's theorem via enriched model categories:

• Bertrand Guillou, Peter May, Jonathan Rubin, Enriched model categories in equivariant contexts, Homology, Homotopy and Applications 21 (1), 2019 (arXiv:1307.4488, arXiv:10.4310/HHA.2019.v21.n1.a10)

Related $n$Lab entries

• stable homotopy theory

• equivariant homotopy theory (Bredon cohomology, equivariant stable homotopy theory, rational equivariant stable homotopy theory)

• higher algebra

• model category

• operad

• infinite loop space