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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:

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

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:

On operads and motives:

On equivariant stable homotopy theory:

On equivariant complex oriented cohomology theory:

On tensor triangulated categories and traces:

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

On six operations and Wirthmüller contexts:

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:

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

category: people