Smoothing fibre bundles and diffeomorphism groups of discs

Ponente: Manuel Krannich
Institución: University of Münster
Tipo de Evento: Investigación

Cuándo	09/12/2021 de 13:00 a 14:00
Dónde	En linea (zoom)
Agregar evento al calendario	vCal iCal

Given a fibre bundle p: E -> B of topological manifolds with d-dimensional fibres, one might ask whether p is fibrewise homeomorphic to a smooth bundle. If d≠4, then there is a strategy to answer this question based on smoothing and obstruction theory. The main limiting factor in this approach is that it requires knowledge of the homotopy groups of the topological group of diffeomorphisms of a closed d-disc. The study of these homotopy groups has quite a history in geometric topology and turns out to be related to algebraic K- and L-theory, stable homotopy theory, and the combinatorics of finite graphs.

In this talk I will explain the relation between smoothing fibre bundles and the homotopy groups of diffeomorphisms of discs, survey the state of the art in the computation of the latter, and explain aspects of recent joint work with Oscar Randal-Williams.