# Bonn Topology Group - Abstracts

General Information - Members - Activities - Topology Seminar

### Talk

16 January 2018

MANUEL KRANNICH (University of Copenhagen): On characteristic classes of exotic manifold bundles

### Abstract

The well-studied inertia group of a closed manifold M captures the behavior of the diffeomorphism type of M when changing the smooth structure of M on a codimension zero disc, that is, when taking the connected sum M#S with an exotic sphere S. Instead of comparing their diffeomorphism types, one might try to compare the group of diffeomorphisms of M and M#S. However, the space of diffeomorphisms Diff(M) can be shown to naturally decompose as a twisted product whose factors are, up to homotopy, insensitive to replacing M with M#S. This suggests that it is hard to detect the possible exotic nature of M#S by means of homotopical properties of its group of diffeomorphisms. Using recent progress in manifold theory by Galatius and Randal-Williams, together with computations in stable homotopy theory, I will discuss results on the behavior of the cohomology of BDiff(M) when replacing M with M#S.

Back to seminar page

## News

Gerd Faltings elected member of the Order Pour le MÃ©rite

Geordie Williamson receives the Max Planck-Humboldt Research Award 2024

ERC Starting Grant for Markus Hausmann

EMS Prize 2024 for Jessica Fintzen

Bonn mathematics performs excellently again in QS ranking

Stefan Schwede is invited speaker at the ECM 2024 in Sevilla

Jessica Fintzen wins Cole Prize

Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023

Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society

Peter Scholze elected as Foreign Member of the Royal Society