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- W4297662457 abstract "We give a new construction of the equivariant $K$-theory of group actions (cf. Barwick et al.), producing an infinite loop $G$-space for each Waldhausen category with $G$-action, for a finite group $G$. On the category $R(X)$ of retractive spaces over a $G$-space $X$, this produces an equivariant lift of Waldhausen's functor $A(X)$, and we show that the $H$-fixed points are the bivariant $A$-theory of the fibration $X_{hH}to BH$. We then use the framework of spectral Mackey functors to produce a second equivariant refinement $A_G(X)$ whose fixed points have tom Dieck type splittings. We expect this second definition to be suitable for an equivariant generalization of the parametrized $h$-cobordism theorem." @default.
- W4297662457 created "2022-09-30" @default.
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- W4297662457 date "2016-09-12" @default.
- W4297662457 modified "2023-10-18" @default.
- W4297662457 title "Equivariant $A$-theory" @default.
- W4297662457 doi "https://doi.org/10.48550/arxiv.1609.03429" @default.
- W4297662457 hasPublicationYear "2016" @default.
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