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.
Christine Kinsey , ``Topology of Surfaces" , Undergraduate Texts in Mathematics (1993)
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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.