Manifolds of positive scalar curvature and conformal cobordism theory

For a supergoup gamma, we study closed gamma-manifolds with positive conformal classes. We use the relative Yamabe invariant from [2] to define the conformal cobordism relation on the category of such manifolds. We prove that the corresponding conformal cobordism groups Pos(*)(conf)(gamma) are isomorphic to the cobordism groups Pos(*)(gamma) defined by Stolz in [19]. As a corollary, we show that the conformal concordance relation on positive conformal classes coincides with the standard concordance relation on positive scalar curvature metrics. Our main technical tools come from analysis and conformal geometry.