A quotient restriction theorem for actions of real reductive groups

Abstract

Abstract. We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X/ /G for the G-action, we introduce a stratification which is defined with respect to orbit types of closed orbits. Our main result is a description of the quotient X/ /G in terms of quotients by normalizer subgroups associated to the stratification.