May 11 2020

Geometry, Topology and Dynamics Seminar: Positive Scalar Curvature and Foliations, by Moulay-Tahar Benameur

May 11, 2020

3:00 PM - 3:50 PM

Location

636 SEO

Address

Chicago, IL

Moulay-Tahar Benameur (Institut Montpellierain Alexander Grothendieck, Université de Montpellier, France ): Positive Scalar Curvature and Foliations

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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Contact

James Heitsch

Date posted

Feb 18, 2020

Date updated

Feb 18, 2020

Speakers

Moulay-Tahar Benameur | (Institut Montpellierain Alexander Grothendieck, Université de Montpellier, France )