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Klein four-slices of HF_2

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HHHW02 - Equivariant and motivic homotopy theory

The slice filtration is a filtration of equivariant spectra analogous to the Postnikov tower that was developed by Hill, Hopkins, and Ravenel in their solution to the Kervaire invariant-one problem. Since that time there have been several new developments, many dealing with cyclic groups. In this talk, we will focus our attention on a noncyclic group! After recalling a few essential definitions and previous results, we will investigate some computational tools that allow us to leverage homotopy results of Holler-Kriz to determine the slices of integer suspensions of HF_2 when our group is the Klein four group. We will end with a few slice tower and spectral sequence examples demonstrating the patterns that arise in the filtration. This is joint work with Bert Guillou.

This talk is part of the Isaac Newton Institute Seminar Series series.

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