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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)

Abstract: 

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

Topic

Science and Technology

Audience

Current students, Faculty

Website

https://www.math.ksu.edu/events/

Department
Mathematics, Department of
Hashtag

#TopologySeminar

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