Equivariant Unfoldings of G-Stratified Pseudomanifolds
Abstract
Description
For any abelian compact Lie group $G$, we introduce a family of $G$-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 $G$ act on a manifold $M$, we find a equivariant unfolding of $M$ which induces a canonical unfolding on the $k$-orbits space for every closed subgroup $K$ of $G$.
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
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