Stratified obstruction systems for equivariant moduli problems and invariant Euler cycles

Yang, Xiangdong

doi:10.2140/agt.2015.15.287

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Stratified obstruction systems for equivariant moduli problems and invariant Euler cycles

Xiangdong Yang

Algebraic & Geometric Topology 15 (2015) 287–318

DOI: 10.2140/agt.2015.15.287

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

References

Publication

Received: 30 December 2013

Revised: 30 June 2014

Accepted: 10 August 2014

Published: 23 March 2015

Authors

Xiangdong Yang
Department of Mathematics Sichuan University Chengdu, 610064 China

Volume 15, issue 1 (2015)