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Contractible 3-manifolds and Positive scalar curvature45m2.058
It is not known whether a contractible 3-manifold admits a complete metric of positive scalar curvature. For example, the Whitehead manifold is a contractible 3-manifold but not homeomorphic to $R^3$. In this talk, we will present my proof that it does not have a complete metric of non-negative scalar curvature. I will further explain that a contractible genus one 3-manifold, a notion introduced by McMillan, does not have a complete metric of non-negative scalar curvature.
Curvature bounds for regularized riemannian metrics45m2.058
(University of Fribourg)
H-Space multiplications on metrics of positive scalar curvature45m2.058
Moduli spaces of metrics of nonnegative sectional curvature on homotopy RP^745m0.019
(University of Fribourg)
Moduli Spaces of Ricci-Flat Metrics on K3 Surfaces45m0.019
Scalar positive immersions45m0.019
As shown by Gromov-Lawson and Stolz the only obstruction to the existence of positive scalar curvature metrics on closed simply connected manifolds in dimensions at least five appears on spin manifolds, and is given by the non-vanishing of the alpha-genus of Hitchin.
When unobstructed we shall realise a positive scalar curvature metric by an immersion into Euclidean space whose dimension is uniformly close to the classical Whitney upper bound for smooth immersions.
Our main tool is an extrinsic counterpart of the well-known Gromov-Lawson surgery procedure for constructing positive scalar curvature metrics.