Bonn Topology Group - Abstracts

General Information - Members - Activities - Topology Seminar

Talk

November 6th 2018
Jens Reinhold (Standford University): Manifold bundles over surfaces.

Abstract

It is well-known that the signature of a manifold fibering over a surface is divisible by 4. One may ask if restricting the diffeomorphism type of the fiber M results in stronger divisibility constraints. I will present a synopsis of joint work with M.Krannich on the classification of total spaces of such fibre bundles if M is highly connected and almost parallelizable, including a calculation of their characteristic numbers. As a corollary, we determine the occuring signatures; it turns our that signature 4 is viable only in dimensions 4, 8 and 16. I will end by describing a basis of the second integral cohomology of BDiff(M) up to torsion in terms of generalized Miller-Morita-Mumford classes.

Back to seminar page