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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.
Keywords: equivariant infinite loop spaces, permutative categories, equivariant algebraic K-theory
Guillou, Bertrand 1 ; May, Peter 2
@article{10_2140_agt_2017_17_3259,
author = {Guillou, Bertrand and May, Peter},
title = {Equivariant iterated loop space theory and permutative {G{\textendash}categories}},
journal = {Algebraic and Geometric Topology},
pages = {3259--3339},
publisher = {mathdoc},
volume = {17},
number = {6},
year = {2017},
doi = {10.2140/agt.2017.17.3259},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3259/}
}
TY - JOUR AU - Guillou, Bertrand AU - May, Peter TI - Equivariant iterated loop space theory and permutative G–categories JO - Algebraic and Geometric Topology PY - 2017 SP - 3259 EP - 3339 VL - 17 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3259/ DO - 10.2140/agt.2017.17.3259 ID - 10_2140_agt_2017_17_3259 ER -
%0 Journal Article %A Guillou, Bertrand %A May, Peter %T Equivariant iterated loop space theory and permutative G–categories %J Algebraic and Geometric Topology %D 2017 %P 3259-3339 %V 17 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3259/ %R 10.2140/agt.2017.17.3259 %F 10_2140_agt_2017_17_3259
Guillou, Bertrand; May, Peter. Equivariant iterated loop space theory and permutative G–categories. Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3259-3339. doi: 10.2140/agt.2017.17.3259
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