Continuous functors as a model for the equivariant stable homotopy category
| Autor: | Andrew J. Blumberg |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Pure mathematics
Functor equivariant infinite loop space theory Homotopy category excisive functors Lie group 55P42 55P47 55P91 55P91 Mathematics::Algebraic Topology Infinite loop Mathematics::K-Theory and Homology Mathematics::Category Theory 55P42 FOS: Mathematics 55P47 Equivariant map Algebraic Topology (math.AT) Atiyah duality Mathematics - Algebraic Topology Geometry and Topology Equivalence (formal languages) Mathematics |
| Zdroj: | Algebr. Geom. Topol. 6, no. 5 (2006), 2257-2295 |
| ISSN: | 2257-2295 |
| DOI: | 10.48550/arxiv.math/0505512 |
| Popis: | 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. Comment: This is the version published by Algebraic & Geometric Topology on 8 December 2006 |
| Databáze: | OpenAIRE |
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