Abstract
AbstractLet W be a compact simply connected triangulated manifold with boundary and let 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 configuration space of two points in a compact manifold with boundary under 2-connectedness hypotheses. Also, we exhibit nice explicit models of these configuration spaces for a large class of compact manifolds.
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