Rational Models of the Complement of a Subpolyhedron in a Manifold with Boundary

Abstract

Abstract. Let W be a compact simply connected triangulated manifold with boundary and K ⊂ W be a subpolyhedron. We construct an algebraic model of the rational homotopy type of W K out of a model of the map of pairs (K, K ∩ ∂W) ↪ (W, ∂W) under some high codimension hypothesis.We deduce the rational homotopy invariance of the con guration space of two points in a compact manifold with boundary under -connectedness hypotheses. Also, we exhibit nice explicit models of these con guration spaces for a large class of compact manifolds.