Degree product formula in the case of a finite group action

TL;DR

This paper provides a concise proof of the degree product formula for local equivariant maps in the context of finite group actions on finite-dimensional orthogonal representations, contributing to the understanding of equivariant degrees.

Contribution

It offers a simplified proof of the degree product formula for equivariant degrees, enhancing theoretical understanding in the field of finite group actions on representations.

Findings

Short proof of the degree product formula

Clarification of properties of equivariant degrees

Advancement in theoretical framework for group actions

Abstract

Let $V, W$ be finite-dimensional orthogonal representations of a finite group $G$. The equivariant degree with values in the Burnside ring of $G$ has been studied extensively by many authors. We present a short proof of the degree product formula for local equivariant maps on $V$ and $W$.