Geometric Analysis and Topology Seminar

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Torsion obstructions to positive scalar curvature

Speaker: Bernhard Hanke, Universität Augsburg

Location: Warren Weaver Hall 412 (special time and location)

Date: Friday, December 15, 2023, 10 a.m.

Synopsis:

The geometric, topological and analytic implications of scalar curvature constraints have been an active area of research for many years. In 1998, Thomas Schick discovered a purely homological obstruction to the existence of positive scalar curvature metrics on oriented closed smooth manifolds in terms of torality properties of their fundamental classes. We will combine this obstruction with the enlargeability obstruction to positive scalar curvature metrics introduced by Gromov and Lawson in the 1980s.

As an application we construct new examples of manifolds which do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics. 

Several fundamental questions remain open. The most important is whether toral manifolds of dimension at least 4 with finite fundamental groups of odd order admit positive scalar curvature metrics. 

This talk is based on joint work with Misha Gromov.