Geodesic
Rational Models of the Complement of a Subpolyhedron in a Manifold with Boundary
Canadian journal of mathematics, Tome 70 (2018) no. 2, pp. 265-293

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DOI

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 compactmanifold with boundary under 2-connectedness hypotheses. Also, we exhibit nice explicit models of these configuration spaces for a large class of compact manifolds.
DOI : 10.4153/CJM-2017-021-3
Mots-clés : 55P62, 55R80, Lefschetz duality, Sullivan model, configuration space 
Bulens, Hector Cordova; Lambrechts, Pascal; Stanley, Don. Rational Models of the Complement of a Subpolyhedron in a Manifold with Boundary. Canadian journal of mathematics, Tome 70 (2018) no. 2, pp. 265-293. doi: 10.4153/CJM-2017-021-3
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     author = {Bulens, Hector Cordova and Lambrechts, Pascal and Stanley, Don},
     title = {Rational {Models} of the {Complement} of a {Subpolyhedron} in a {Manifold} with {Boundary}},
     journal = {Canadian journal of mathematics},
     pages = {265--293},
     year = {2018},
     volume = {70},
     number = {2},
     doi = {10.4153/CJM-2017-021-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-021-3/}
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