Equivariant Iterated Loop Space Theory and Permutative G–Categories

Authors

Bertrand J. Guillou, University of KentuckyFollow
J. Peter May, University of Chicago

Abstract

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.

Document Type

Article

Publication Date

10-4-2017

Notes/Citation Information

Published in Algebraic & Geometric Topology, v. 17, issue 6, p. 3259-3339.

The publisher has granted the permission for posting the article here.

Digital Object Identifier (DOI)

https://doi.org/10.2140/agt.2017.17.3259

Funding Information

Guillou was supported by Simons Collaboration Grant 282316.

Repository Citation

Guillou, Bertrand J. and May, J. Peter, "Equivariant Iterated Loop Space Theory and Permutative G–Categories" (2017). Mathematics Faculty Publications. 33.
https://uknowledge.uky.edu/math_facpub/33