Stable equivariant abelianization, its properties, and applications |
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Authors: | Pedro F dos Santos |
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Institution: | a Department of Mathematics, Instituto Superior Técnico, Avenida Rovisco Pais, Lisboa 1049-001, Portugal b Department of Mathematics, Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601, USA |
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Abstract: | Let G be a finite group. For a based G-space X and a Mackey functor M, a topological Mackey functor is constructed, which will be called the stable equivariant abelianization of X with coefficients in M. When X is a based G-CW complex, is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold-Thom theorem. Applying a variant of Elmendorf's construction, we get a model for the Eilenberg-Mac Lane spectrum HM. The proof uses a structure theorem for Mackey functors and our previous results. |
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Keywords: | Mackey functor Stable equivariant abelianization Infinite loop space Equivariant Eilenberg-Mac Lane spectra |
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