## Diffeomorphisms of discs and positive scalar curvature

Diarmuid Crowley (Melbourne)

Abstract

Let $${\rm Diff}(D^k)$$ be the space of diffeomorphisms of the $$k$$-disc fixing the boundary pointwise. Understanding the topology of $${\rm Diff}(D^k)$$ is a longstanding and difficult problem in differential topology. In this talk I will report on recent work with Thomas Schick and Wolfgang Steimle which shows that for $$k > 5$$ the homotopy groups $$\pi_* {\rm Diff}(D^k)$$ have non-zero $$8$$-periodic $$2$$-torsion detected in real K-theory. I will then discuss applications to the space of positive scalar curvature metrics on spin manifolds of dimension $$6$$ or greater.