Stratified obstruction systems for equivariant moduli problems and invariant Euler cycles

Abstract

The purpose of this paper is to study finite-dimensional equivariant moduli problems from the viewpoint of stratification theory. We show that there exists a stratified obstruction system for a finite-dimensional equivariant moduli problem. In addition, we define a coindex for a $G$–vector bundle that is determined by the $G$–action on the vector bundle and prove that if the coindex of an oriented equivariant moduli problem is bigger than $1$, then we obtain an invariant Euler cycle via equivariant perturbation. In particular, we get a localization formula for the stratified transversal intersection of $S^1$–moduli problems.