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

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 $T$-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.