Rational models of the complement of a subpolyhedron in a manifold with boundary

Abstract

Let W be a compact simply connected triangulated manifold with boundary and $K\subset W$ be a subpolyhedron. We construct an algebraic model of the rational homotopy type of the complement $W\setminus K$ out of a model of the map of pairs $(K,K\cap \partial W)\to (W,\partial W)$ under some high codimension hypothesis. We deduce the rational homotopy invariance of the configuration space of two points in a compact manifold with boundary under 2-connectedness hypotheses. Also, we exhibit nice explicits models of these configuration spaces for a large class of compact manifolds.

28 pages