Topology seminar: The Disc-structure space, Part II
Speakers: A. Kupers, University of Toronto (and M. Krannich, Karlsruhe Institute of Technology)
The classical approach to studying the category of manifolds and diffeomorphisms is to compare it to the category of spaces and homotopy equivalences, by assigning a manifold its underlying space. The information lost in this comparison can be encoded in certain “structure spaces” that are expressible -- in a certain range -- in terms of well-studied infinite loop spaces. More recent developments related to manifold calculus and factorisation homology suggest a different approach, which in addition to the underlying homotopy type of a manifold also takes the homotopy types of all its configuration spaces into account. Again, understanding how much information is lost amounts to studying certain structure spaces: the “Disc-structure spaces”.
This is the second talk in a series of two. After recalling the definition of the Disc-structure spaces, we explain why they have the surprising features stated in the first talk: they are non-trivial infinite loop spaces that depend only little on the underlying manifolds. Part of the proof is a result about automorphisms of the little d-discs operad which is of independent interest.
Friday, July 1 at 2:30pm to 3:20pm