Equivariant iterated loop space theory and permutative G-categories

Bertrand J. Guillou, J. Peter May

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We set up operadic foundations for equivariant iterated loop space theory. We start by building up from a discussion of the approximation theorem and recognition principle for V-fold loop G-spaces to several avatars of a recognition principle for infinite loop G-spaces. We then explain what genuine permutative G-categories are and, more generally, what E-G-categories are, giving examples showing how they arise. As an application, we prove the equivariant Barratt-Priddy-Quillen theorem as a statement about genuine G-spectra and use it to give a new, categorical proof of the tom Dieck splitting theorem for suspension G-spectra. Other examples are geared towards equivariant algebraic K-theory.

Original languageEnglish
Pages (from-to)3259-3339
Number of pages81
JournalAlgebraic and Geometric Topology
Issue number6
StatePublished - Oct 4 2017

Bibliographical note

Publisher Copyright:
© 2017, Mathematical Sciences Publishers. All rights reserved.


  • Equivariant algebraic K-theory
  • Equivariant infinite loop spaces
  • Permutative categories

ASJC Scopus subject areas

  • Geometry and Topology


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