Manifolds of Positive Scalar Curvature and Conformal Cobordism Theory

Details Manifolds of Positive Scalar Curvature and Conformal Cobordism Theory Manifolds of Positive Scalar Curvature and Conformal Cobordism Theory

2000-08-17

arxiv.org/abs/math/0008139v1

Mathematics

Differential Geometry

21 page, 6 fig

Scientific paper

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.

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