Equivariant Unfoldings of G-Stratified Pseudomanifolds
Abstract
For any abelian compact Lie group , we introduce a family of -stratified pseudomanifolds, whose main feature is the preservation of the orbit spaces in the category of stratified pseudomanifolds. Which generalize a previous definition given by R. Popper. We also find a sufficient condition for the existence of equivariant unfoldings, so we have Intersection Cohomology with differential forms, as defined in \cite{S}. Moreover, if act on a manifold , we find a equivariant unfolding of which induces a canonical unfolding on the -orbits space for every closed subgroup of .
Keywords
Cite
@article{arxiv.math/0312213,
title = {Equivariant Unfoldings of G-Stratified Pseudomanifolds},
author = {F. Dalmagro},
journal= {arXiv preprint arXiv:math/0312213},
year = {2007}
}
Comments
This is a paper on geometric topology which generalizes in the stratified context the procedure of Davis for blowing up a smooth manifold along a closed submanifold. We also work in the equivariant category, generalizing a previous definition of R. Popper for $G$-stratified pseudomanifolds. The main applications of this work are intended to the cohomological study of torical actions on stratified pseudomanifolds, as a particular case of iterated stratified circle actions