Mathematics Seminar
Date: Wednesday, 13 Novemeber 2024
Time: 02:00 PM
Venue: Seminar Hall
Universal Stiefel-Whitney Classes for Special Linear Groups
Neha Malik
Chennai Mathematical Institute.
13-11-24

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Abstract

Orthogonal representations $\pi$ of a finite group $G$ have cohomological invariants $w_k(\pi)$ living in the mod 2 group cohomology, called Stiefel-Whitney Classes (SWCs). We have computed their sum, called the total SWC of $\pi$, for $G=SL(n,q)$ when $n,q$ are odd. As a consequence, we obtain a restriction result that allows for a ???universal??? calculation of $w_k$ in terms of character values, valid for all $n$ sufficiently large. We have explicitly worked out $w_4$ and $w_8$. This is joint work with Prof. Steven Spallon.