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Topology seminar: The Disc-structure space, Part I

Speakers: M. Krannich, Karlsruhe Institute of Technology (and A. Kupers, University of Toronto)


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”.


In this first talk in a series of two, we will motivate and explain the above, leading to a precise statement of our main result that these Disc-structure spaces are nontrivial infinite loop spaces that depend only little on the underlying manifolds -- without dependence on a range.

Friday, June 24 at 2:30pm to 3:20pm

Event Type

Lecture, Colloquia, Seminar


Science and Technology


Current students, Faculty



Mathematics, Department of


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