Occupants in manifolds

TL;DR

This paper explores a homotopical formula for the space M minus K in smooth manifolds, using functor calculus to relate it to subspaces M minus S for finite subsets S of K.

Contribution

It introduces a novel application of functor calculus to derive homotopical formulas for complements of subsets in smooth manifolds.

Findings

Derived a homotopical formula for M minus K

Connected the complement space to finite subset subspaces

Applied functor calculus to manifold topology

Abstract

Let K be a subset of a smooth manifold M. In some cases functor calculus methods lead to a homotopical formula for M minus K in terms of the subspaces M minus S, where S runs through the finite subsets of K.