A NEW FORMULATION OF THE EQUIVARIANT SLICE FILTRATION WITH APPLICATIONS TO C-p-SLICES

摘要

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/vertical bar H vertical bar-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-pn-spectra.