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arXiv · 1703.02684

Enlargeability, foliations, and positive scalar curvature

Moulay-Tahar Benameur·James L. Heitsch
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Abstract

We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show: that a spin foliation with Hausdorff homotopy groupoid of an enlargeable manifold admits no PSC metric; that any metric of PSC on such a foliation is bounded by a multiple of the reciprocal of the foliation K-area of the ambient manifold; and that Connes' vanishing theorem for characteristic numbers of PSC foliations extends to a vanishing theorem for Haefliger cohomology classes.

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Moulay-Tahar Benameur, James L. Heitsch. 2017-03-08. Enlargeability, foliations, and positive scalar curvature. https://arxiv.org/abs/1703.02684

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