Equivariant characteristic classes of singular hypersurfaces

In this paper, we introduce definitions for the integrated equivariant Milnor number [Formula: see text] and the equivariant Milnor class [Formula: see text], for singular hypersurfaces. We prove that the [Formula: see text] are constant on the strata in a Whitney stratification of [Formula: see text], along with the correlation [Formula: see text] for hypersurfaces hosting isolated singularities [Formula: see text], where [Formula: see text] denotes the [Formula: see text]th equivariant Milnor class of [Formula: see text]. We also introduce the equivariant Fulton–Johnson class of singular hypersurfaces. We give an equivariant version of Verdier’s specialization morphism in homology, and also for constructible functions. This is used for finding a relation between equivariant Fulton–Johnson and Schwartz–MacPherson classes.