Topology Seminar: Anna Cepek

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 S^1 and R^n in terms of the combinatorially defined parasimplex category and Joyal’s category Theta_n, respectively.