Volume 15, issue 1 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 S1–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