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Rational Models of the Complement of a Subpolyhedron in a Manifold with Boundary
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 2 / 01 April 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 265-293
- Print publication:
- 01 April 2018
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- Article
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Let
$W$ be a compact simply connected triangulated manifold with boundary and let 
$K\,\subset \,W$ be a subpolyhedron. We construct an algebraic model of the rational homotopy type of 
$W\text{ }\!\!\backslash\!\!\text{ K}$ out of a model of the map of pairs 
$\left( K,\,K\cap \partial W \right)\,\to \,\left( W,\,\partial W \right)$ 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.
