Classification of locally standard $T$-pseudomanifolds over topological stratified pseudomanifolds

Yuya Koike; Shintaro Kuroki

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arXiv · 2511.10153

Classification of locally standard $T$-pseudomanifolds over topological stratified pseudomanifolds

Yuya Koike·Shintaro Kuroki

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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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Yuya Koike, Shintaro Kuroki. 2025-11-13. Classification of locally standard $T$-pseudomanifolds over topological stratified pseudomanifolds. https://arxiv.org/abs/2511.10153

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