Configuration spaces of the circle and Euclidean spaces
Talk by Anna Cepek (Graduate Student in Mathematical Sciences, MSU) - Public PhD Dissertation Defense
4/8/2019 Wilson Hall 1-144 4:10-5:00pm
We approach manifold topology by examining configurations of finite subsets of manifolds. The homotopy-types of such configurations organize as an ∞-category, the construction of which makes use of stratified spaces and exit-path ∞-categories thereof. The goal of this talk is to supply the constructions of these ∞-categories and to identify these ∞-categories in the case of S1 and Rn in terms of the combinatorially defined parasimplex category and Joyal’s category Θn, respectively.