On Normal Stratified Pseudomanifolds
G. Padilla

TL;DR
This paper improves the theory of stratified pseudomanifolds by constructing a functorial normalization that preserves intersection homology and satisfies stronger local triviality conditions, extending previous results to broader settings.
Contribution
It proves the existence of a stronger, locally trivial normalization for stratified pseudomanifolds, extending Borel's results to more general cases and providing an explicit, functorial construction.
Findings
Constructed a normalization satisfying stronger local triviality conditions.
Extended Borel's normalization result to broader classes of stratified pseudomanifolds.
Provided an explicit, functorial normalization construction.
Abstract
A stratified pseudomanifold is normal if its links are connected. A normalization of a stratified pseudomanifold is a normal stratified pseudomanifold together with a finite-to-one projection satisfying a local condition related to the fibers. The map n preserves the intersection homology. Following Borel any pl-stratified pseudomanifod has a normalization in the above sense. In this parper: 1.- We prove that the map can be required to satisfy a stronger condition: it is a locally trivial stratified morphism preserving the conical structure transverse to the strata. 2.- We extend Borel's result for any topological stratified pseudomanifold and for a family of perversities which is larger than the usual one. 3.- We make an explicit construction of such a normalization. We give a detailed description of the normalizer's stratification. 4.- We prove that our…
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications
