Bonn Topology Group - Abstracts

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Talk

May 28, 2024
Vignesh Subramanian (Max Planck Institute for Mathematics): Categorification of Smith Theory

Abstract

Given an E_\infty-algebra A over F_p, there exists a homotopically coherent version of the Frobenius map on A, called the Tate valued Frobenius A \to A^tC_p. In this talk, I will recall the notion of a Frobenius perfect F_p-algebra and construct associated perfection A^\flat, which we refer to as tilting. We will provide an explicit formula for computing the homotopy groups of the tilt via power operations. As an application, consider a finite G-CW complex X, where G is a p-group. I will offer a method to recover the p-local homotopy type of the genuine fixed point X^G from the Borel equivariant cohomology of X. This application can be viewed as a categorification of Smith theory, which plays a significant role in the ideas surrounding the proof of the Sullivan conjecture. This is joint work with Robert Burklund.