  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 where the subset $K$ is assumed to be a smooth submanifold of $M$
and uses his generalization of manifold calculus adapted for simplicial
complexes.
