Geometry, Topology and Dynamics Seminar
Roman Sauer
U Chicago
Amenable Covers, Minimal Volume and L^2-Betti numbers of aspherical manifolds
Abstract: We present a proof of an inequality between the minimal volume and the L^2-
Betti
numbers of closed, aspherical manifolds which was claimed by Gromov. Moreover,
we show a new L^2-vanishing theorem for amenable covers that generalizes a
theorem of Cheeger and Gromov. The methods involve, perhaps surprisingly, group
actions on probability spaces, Gaboriau's simplicial complexes of measured
equivalence relations, and other themes of measurable group theory.
Monday November 6, 2006 at 3:00 PM in SEO 512