SMS scnews item created by Haotian Wu at Fri 7 Apr 2017 2039
Type: Seminar
Distribution: World
Expiry: 7 Oct 2017
Calendar1: 13 Apr 2017 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Geometry & Topology Seminar: Diarmuid Crowley -- Diffeomorphisms of discs and positive scalar curvature
Auth: haotianw@como.maths.usyd.edu.au

# Diffeomorphisms of discs and positive scalar curvature

### Diarmuid Crowley (Melbourne)

Thursday 13 Apr 12:00–13:00 in Carslaw 535A.

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.