Units of equivariant ring spectra
| Autor: | Rekha Santhanam |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Ring (mathematics)
Pure mathematics equivariant $\Gamma$–space Group (mathematics) 55P91 Mathematics::Algebraic Topology Spectral line 55P91 55P47 55P42 Mathematics::K-Theory and Homology Mathematics::Category Theory 55P42 FOS: Mathematics Equivariant map 55P47 Algebraic Topology (math.AT) equivariant spectra 55P48 Geometry and Topology Mathematics - Algebraic Topology Mathematics::Symplectic Geometry Mathematics equivariant infinite loop space |
| Zdroj: | Algebr. Geom. Topol. 11, no. 3 (2011), 1361-1403 |
| Popis: | It is well known that very special $\Gamma$-spaces and grouplike $\E_\infty$ spaces both model connective spectra. Both these models have equivariant analogues. Shimakawa defined the category of equivariant $\Gamma$-spaces and showed that special equivariant $\Gamma$-spaces determine positive equivariant spectra. Costenoble and Waner showed that grouplike equivariant $\E_\infty$-spaces determine connective equivariant spectra. We show that with suitable model category structures the category of equivariant $\Gamma$-spaces is Quillen equivalent to the category of equivariant $\E_\infty$ spaces. We define the units of equivariant ring spectra in terms of equivariant $\Gamma$-spaces and show that the units of an equivariant ring spectrum determines a connective equivariant spectrum. Comment: More detailed introduction, added appendix C |
| Databáze: | OpenAIRE |
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