Open Access

Sven Führing

• We introduce a smooth variation of Baas-Sullivan theory, yielding an interpretation of singular homology and connective real K-theory by smooth manifolds with additional structures on their boundaries, called singular manifolds. This enables us to give a proof of the so-called Homology Theorem (with 2 inverted) which in many cases reduces the existence question of positive scalar curvature metrics on closed manifolds to the study of the singular homology resp. connective real K-theory of their fundamental groups. Subsequently, we consider the question of positive scalar curvature on simply connected singular manifolds and show existence theorems corresponding to statements in the closed case. Within the scope of our treatment of non-simply connected singular manifolds, we finally introduce the notion of a positive homology class, and we show that the atoral classes of the singular homology of an elementary Abelian p-group, p an odd prime, are positive.