In dimensions ≤3, locally standard T-pseudomanifolds are classified by characteristic data without the homotopy equivalence condition, and manifold cases are characterized via orbit spaces.
Classification of locally standard $T$-pseudomanifolds over topological stratified pseudomanifolds
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abstract
We introduce the notion of a locally standard $T$-pseudomanifold, a class that generalizes both complete toric varieties and locally standard $T$-manifolds. The main goal of this paper is to show that locally standard $T$-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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math.GT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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On $3$-dimensional locally standard $T$-pseudomanifolds
In dimensions ≤3, locally standard T-pseudomanifolds are classified by characteristic data without the homotopy equivalence condition, and manifold cases are characterized via orbit spaces.