Manifolds of Positive Scalar Curvature and Conformal Cobordism Theory

Abstract

We study here compact manifolds with positive scalar curvature metrics. We use the relative Yamabe invariant from math.DG/0008138 to define the conformal cobordism relation on the category of such manifolds. We prove that corresponding conformal cobordism groups $\Pos_n^{\conf}(\gamma)$ are isomorphic to the cobordism groups $\Pos_n(\gamma)$ defined topologically by S. Stolz. As a corollary we show that the conformal concordance of positive scalar curvature metrics coincides with the standard concordance relation. Our main technical tools came from the analysis and conformal geometry.