Manifold of Positive Scalar Curvature and Conformal Cobordism Theory

摘要

The authors study compact manifolds with positive scalar curvature metrics. Theauthors use the relative invariant to define the conformal cobordism relation on the category of such manifolds. The authors prove that corresponding conformal cobordism groups Pos(sub n)(sup Conf)(Gamma) are isomorphic to the cobordism groups Posn(Gamma) defined topologically by S. Stolz. As a corollary the authors show that the conformal concordance of positive scalar curvature metrics coincides with the standard concordance relation. The authors' main technical tools came from the analysis and conformal geometry.