Product Property of Equivariant Degree Under the Action of a Compact Abelian Lie Group

Abstract

We study local equivariant maps on real finite dimensional orthogonal representations of a compact abelian Lie group G. Equivariant degree $$\deg _G$$ is an invariant applied to determine whether a given map has zeros. The goal of this paper is to present a complete, straightforward proof of the product property of $$\deg _G$$ . For that purpose, we use the otopy classification and distinguish a special kind of map in each class.