location:  Publications → journals → CJM
Abstract view

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

Published:2017-11-07
Printed: Apr 2018
• 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
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 55P62 - Rational homotopy theory 55R80 - Discriminantal varieties, configuration spaces

 top of page | contact us | privacy | site map |