A simply connected spin pseudomanifold with homogeneous link admits a well-adapted positive scalar curvature wedge metric exactly when two alpha-invariants vanish, under a dimension bound and one of two bordism conditions.
Banagl, Topological invariants of stratified spaces, Springer Monographs in Mathematics, Springer Verlag, Ber lin, 2007
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Positive scalar curvature on simply connected spin pseudomanifolds
A simply connected spin pseudomanifold with homogeneous link admits a well-adapted positive scalar curvature wedge metric exactly when two alpha-invariants vanish, under a dimension bound and one of two bordism conditions.