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

2015/05/18 by Hector Cordova Bulens, Bulens, Hector Cordova, Pascal Lambrechts +3
Mathematics · #55P62 #55R80 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P62 #msc:55R80

paper · pdf · doi:10.48550/arxiv.1505.04816

28 pages

arxiv created 2015/05/18 · openalex publication_date 2015/05/18 · arxiv updated 2015/05/20 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Let W be a compact simply connected triangulated manifold with boundary and K ⊂ W be a subpolyhedron. We construct an algebraic model of the rational homotopy type of the complement W ∖ K out of a model of the map of pairs (K, K ∩ ∂ W) → (W,∂ 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 explicits models of these configuration spaces for a large class of compact manifolds.

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