nLab
Peter May

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 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

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

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 cohomology and equivariant homotopy theory:

On highly structured spectra:

On H-infinity ring spectra:

On equivariant bundles:

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

On equivariant bundles with abelian structure group:

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

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:

On equivariant complex oriented cohomology theory:

On tensor triangulated categories and traces:

On parametrized stable homotopy theory:

On enriched model category theory:

On higher category theory:

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:

category: people

Last revised on June 11, 2021 at 04:53:05. See the history of this page for a list of all contributions to it.