nLab
Peter May

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 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 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-infinity ring spectra:

• R. Bruner, Peter May, James McClure, M. Steinberger, $H_\infty$-Ring Spectra and their Applications, Lecture Notes in Mathematics 1176, Springer 1986 (doi:10.1007/BFb0075405, 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 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 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)

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

category: people