Manifolds of Positive Scalar Curvature and Conformal Cobordism Theory
Kazuo Akutagawa, Boris Botvinnik
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 n(γ) are isomorphic to the cobordism groups n(γ) 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.
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