Equivariant Unfoldings of G-Stratified Pseudomanifolds · arXivDesk
math/0312213Dec 10, 2003This 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
Equivariant Unfoldings of G-Stratified Pseudomanifolds
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 S. Moreover, if G act on a manifold M, we find a equivariant unfolding of M which induces a canonical unfolding on the k