A NEW FORMULATION OF THE EQUIVARIANT SLICE FILTRATION WITH APPLICATIONS TO Cp-SLICES.

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 Hgeometric fixed points are (n/|H| - 1)-connected. We use this to determine when smashing with a virtual representation sphere SV induces an equivalence between various slice categories. Using this, we give an explicit formula for the slices for an arbitrary Cp-spectrum and show how a very small number of functors determine all of the slices for Cpn-spectra. [ABSTRACT FROM AUTHOR]