Classification of locally standard $T$-pseudomanifolds over topological stratified pseudomanifolds
Yuya Koike, Shintaro Kuroki

TL;DR
This paper introduces locally standard T-pseudomanifolds over topological stratified pseudomanifolds and classifies them up to equivariant homeomorphism using characteristic data, extending quasitoric manifold classification.
Contribution
It generalizes the classification of quasitoric manifolds to a broader class of pseudomanifolds using characteristic data.
Findings
Locally standard T-pseudomanifolds are classified by characteristic data.
The classification extends Davis-Januszkiewicz's work on quasitoric manifolds.
The paper establishes conditions under which classification is complete.
Abstract
We introduce the notion of a locally standard -pseudomanifold, a class that generalizes both complete toric varieties and locally standard -manifolds. The main goal of this paper is to show that locally standard -pseudomanifolds over topological stratified pseudomanifolds satisfying certain conditions are completely classified, up to (weakly) equivariant homeomorphism, by their characteristic data. This result extends the classification of quasitoric manifolds by Davis-Januszkiewicz.
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