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

Published online by Cambridge University Press:  20 November 2018

Hector Cordova Bulens ,
Pascal Lambrechts  and
Don Stanley
Hector Cordova Bulens
Affiliation:
IRMP, Université catholique de Louvain, 2 Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium e-mail: hectorcordovabulens@gmail.compascal.lambrechts@uclouvain.be
Pascal Lambrechts
Affiliation:
IRMP, Université catholique de Louvain, 2 Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium e-mail: hectorcordovabulens@gmail.compascal.lambrechts@uclouvain.be
Don Stanley
Affiliation:
University of Regina, Department of Mathematics and Statistics, College West, Regina e-mail: donald.stanley@uregina.ca
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Abstract

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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.

Keywords

55P6255R80Lefschetz dualitySullivan modelconfiguration space
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 2 , 01 April 2018 , pp. 265 - 293
Copyright
Copyright © Canadian Mathematical Society 2018

References

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