A new formulation of the equivariant slice filtration with applications to $C_p$-slices
| Autor: | Hill, Michael A., Yarnall, Carolyn |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | This paper provides a new way to understand the equivariant slice filtration. We give a new, readily checked condition for determining when a $G$-spectrum is slice $n$-connective. In particular, we show that a $G$-spectrum is slice greater than or equal to $n$ if and only if for all subgroups $H$, the $H$-geometric fixed points are $(n/|H|-1)$-connected. We use this to determine when smashing with a virtual representation sphere $S^V$ induces an equivalence between various slice categories. Using this, we give an explicit formula for the slices for an arbitrary $C_p$-spectrum and show how a very small number of functors determine all of the slices for $C_{p^n}$-spectra. Comment: Final version, to appear in Proceedings of the AMS |
| Databáze: | arXiv |
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