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

  • Hector Cordova Bulens,
    Université catholique de Louvain, Belgium
  • Pascal Lambrechts,
    Université catholique de Louvain, Belgium
  • Don Stanley,
    Department of Mathematics and Statistics, University of Regina
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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 $W\backslash K$ out of a model of the map of pairs $(K,K \cap \partial W)\hookrightarrow (W,\partial W)$ 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 explicit models of these configuration spaces for a large class of compact manifolds.
Keywords: Lefschetz duality, Sullivan model, configuration space Lefschetz duality, Sullivan model, configuration space
MSC Classifications: 55P62, 55R80 show english descriptions Rational homotopy theory
Discriminantal varieties, configuration spaces
55P62 - Rational homotopy theory
55R80 - Discriminantal varieties, configuration spaces
 

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