Geometric non-commutative geometry

Moulay Tahar Benameur; James L. Heitsch

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arXiv · 1909.00063

Geometric non-commutative geometry

Moulay Tahar Benameur·James L. Heitsch

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Abstract

In a recent paper, the authors proved that no spin foliation on a compact enlargeable manifold with Hausdorff homotopy graph admits a metric of positive scalar curvature on its leaves. This result extends groundbreaking results of Lichnerowicz, Gromov and Lawson, and Connes on the non-existence of metrics of positive scalar curvature. In this paper we review in more detail the material needed for the proof of our theorem and we extend our non-existence results to non-compact manifolds of bounded geometry. We also give a first obstruction result for the existence of metric with (not necessarily uniform) leafwise PSC in terms of the A-hat class in Haefliger cohomology.

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Moulay Tahar Benameur, James L. Heitsch. 2019-08-30. Geometric non-commutative geometry. https://arxiv.org/abs/1909.00063

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