Stratified Obstruction Systems for Equivariant Moduli Problems and Invariant Euler cycles

TL;DR

This paper develops a stratified obstruction system framework for finite dimensional equivariant moduli problems, enabling the construction of invariant Euler cycles and localization formulas under certain conditions.

Contribution

It introduces a stratified obstruction system for equivariant moduli problems and defines a coindex to facilitate invariant Euler cycle construction.

Findings

Existence of a stratified obstruction system for equivariant moduli problems

Construction of invariant Euler cycles when coindex > 1

Localization formula for S1-moduli problems

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 which 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 S1-moduli problems.