Journal Article

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

HILL, MICHAEL A., YARNALL, CAROLYN

2018

نظرة عامة

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 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.

• الناشر: American Mathematical Society
• موضوع: G. TOPOLOGY