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

Geometry & Topology Seminar

Diffeomorphisms of discs and positive scalar curvature

Diarmuid Crowley (Melbourne)

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

Please join us for lunch after the talk!

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.