Occupants in simplicial complexes

Abstract

Let $M$ be a smooth manifold and $K\subset M$ be a simplicial complex of codimension at least $3$. Functor calculus methods lead to a homotopical formula of $M\setminus K$ in terms of spaces $M\setminus T$ where $T$ is a finite subset of $K$. This is a generalization of the author’s previous work with Michael Weiss (Contemp. Math. 682, Amer. Math. Soc., Providence, RI (2017) 237–259), where the subset $K$ is assumed to be a smooth submanifold of $M$ and uses his generalization of manifold calculus adapted for simplicial complexes.