Bonn Topology Group - Abstracts

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Talk

June 14, 2022
Manuel Krannich (Karlsruhe Institute of Technology): The Disc-structure space

Abstract

The classical approach to studying the category of manifolds and their diffeomorphisms is to first compare it to a simplified category of bloc -manifolds and then compare the latter to the category of Poincaré complexes. The information lost in each of these steps is encoded in certain structure spaces that are expressible -- in a certain range -- in terms of algebraic K- and L-theory.
More recent developments related to manifold calculus and factorisation homology suggest a different approach, namely to compare the category of manifolds to a variant of the derived category of modules over the little d-discs operad. Again, this amounts to studying certain structure spaces that encode the difference: the Disc-structure spaces.
In this talk, I will explain the above and describe aspects of joint work with A. Kupers in which we show that, in most cases, these Disc-structure spaces are nontrivial infinite loop spaces that depend only little on the underlying manifolds -- without dependence on a range.