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We introduce Riemannian metrics of positive scalar curvature on manifoldswith Baas-Sullivan singularities, prove a corresponding homology invarianceprinciple and discuss admissible products. Using this theory we constructpositive scalar curvature metrics on closed smooth manifolds of dimension atleast five which have odd order abelian fundamental groups, are nonspin andatoral. This solves the Gromov-Lawson-Rosenberg conjecture for a new class ofmanifolds with finite fundamental groups.

Positive scalar curvature on manifolds with odd order abelian fundamental groups