Rational models of the complement of a subpolyhedron in a manifold with boundary
Printed: Apr 2018
Hector Cordova Bulens,
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
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
of compact manifolds.
Lefschetz duality, Sullivan model, configuration space
55P62 - Rational homotopy theory
55R80 - Discriminantal varieties, configuration spaces