\(G\)-symmetric spectra, semistability and the multiplicative norm. (English) Zbl 1420.55023
Summary: In this paper we develop the basic homotopy theory of \(G\)-symmetric spectra (that is, symmetric spectra with a \(G\)-action) for a finite group \(G\), as a model for equivariant stable homotopy with respect to a \(G\)-set universe. This model lies in between Mandell’s equivariant symmetric spectra and the \(G\)-orthogonal spectra of Mandell and May and is Quillen equivalent to the two. We further discuss equivariant semistability, construct model structures on module, algebra and commutative algebra categories and describe the homotopical properties of the multiplicative norm in this context.
MSC:
| 55P91 | Equivariant homotopy theory in algebraic topology |
| 55P43 | Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.) |
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