Equivariant Unfoldings of G-Stratified Pseudomanifolds

Mathematics – Algebraic Topology

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This is a paper on geometric topology which generalizes in the stratified context the procedure of Davis for blowing up a smoo

Scientific paper

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 $G$.

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