Spaces of positive scalar curvature metrics

Speaker(s) Oscar Randal-Williams University of Cambridge
Date 23 September 2021 – 13:00 to 14:00
Venue INI Seminar Room 1
Session Title Spaces of positive scalar curvature metrics
Event [OOEW02] The unity of mathematics: A conference in honour of Sir Michael Atiyah
Abstract

Of the curvature conditions one may consider on Riemannian metrics, positive scalar curvature has the closest connection to topology: it is weak enough that such metrics can be manipulated by topological means, such as surgery on the underlying manifold, but strong enough to allow the spaces of all such metrics to have interesting topology in their own right, which is often probed using index theory. I will survey some recent results, both conceptual and calculational, about the topology of these spaces.

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