Noncommutative Geometry Seminar
Date: March 4, 2022
Time: 08:00AM - 09:00AM
Location: ZOOM
Speaker: Johannes Ebert, University of Münster
Title: Rigidity theorems for the diffeomorphism action on spaces of positive scalar curvature
Abstract: The diffeomorphism group, Diff(M), of a closed manifold acts on the space, R+(M), of positive scalar curvature metrics. For a basepoint, g, we obtain an orbit map σg : Diff(M) → R+(M) which induces a map on homotopy groups (σg)∗ : π∗(Diff(M)) → π∗( R+(M)). The rigidity theorems from the title assert that suitable versions of the map (σg)∗ factors through certain bordism groups. A special case of our main result asserts that (σg)∗ has finite image if M is simply connected, stably parallelizable, and of dimension at least 6. The results of this talk are from joint work of the speaker with Oscar Randal–Williams.
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