Mathematics – Algebraic Topology
Scientific paper
2005-05-24
Algebr. Geom. Topol. 6 (2006) 2257-2295
Mathematics
Algebraic Topology
This is the version published by Algebraic & Geometric Topology on 8 December 2006
Scientific paper
10.2140/agt.2006.6.2257
In this paper, we investigate the properties of the category of equivariant diagram spectra indexed on the category W_G of based G-spaces homeomorphic to finite G-CW-complexes for a compact Lie group G. Using the machinery of Mandell, May, Schwede, and Shipley, we show that there is a "stable model structure" on this category of diagram spectra which admits a monoidal Quillen equivalence to the category of orthogonal G-spectra. We construct a second "absolute stable model structure" which is Quillen equivalent to the "stable model structure". Our main result is a concrete identification of the fibrant objects in the absolute stable model structure. There is a model-theoretic identification of the fibrant continuous functors in the absolute stable model structure as functors Z such that for A in W_G the collection {Z(A smash S^W)} form an Omega-G-prespectrum as W varies over the universe U. We show that a functor is fibrant if and only if it takes G-homotopy pushouts to G-homotopy pullbacks and is suitably compatible with equivariant Atiyah duality for orbit spaces G/H_+ which embed in U. Our motivation for this work is the development of a recognition principle for equivariant infinite loop spaces.
No associations
LandOfFree
Continuous functors as a model for the equivariant stable homotopy category does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Continuous functors as a model for the equivariant stable homotopy category, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuous functors as a model for the equivariant stable homotopy category will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-72907