Stiefel-Whitney Classes Of Representations Of Dihedral Groups

TL;DR

This paper calculates the Stiefel-Whitney classes for dihedral group representations using character theory and provides criteria for lifting representations to double covers and identifying non-trivial Euler classes.

Contribution

It introduces explicit formulas for Stiefel-Whitney classes of dihedral group representations and criteria for lifting and Euler class properties.

Findings

Formulas for Stiefel-Whitney classes in terms of character values.

Criteria for lifting representations to double covers.

Identification of representations with non-trivial mod 2 Euler class.

Abstract

We compute the Stiefel-Whitney Classes for representations of dihedral groups $D_m$ in terms of character values of order two elements. We also provide criteria to identify representations V which lift to the double covers of the orthogonal group O(V ) and those with non-trivial mod 2 Euler class.