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

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.

73 pages, 20 figures; v2: proof of Proposition 14.4 updated, several typos corrected; v3: revised the introduction and added several references; v4: removed Lemma A.2 and revised step 1 in the proof of Lemma 11.3