#### Volume 15, issue 1 (2015)

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Stratified obstruction systems for equivariant moduli problems and invariant Euler cycles

### Xiangdong Yang

Algebraic & Geometric Topology 15 (2015) 287–318
##### 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.

##### Keywords
equivariant vector bundle, equivariant moduli problem, Euler cycle
##### Mathematical Subject Classification 2010
Primary: 57R22, 57R91