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Rational model of the configuration space of two points in a simply connected closed manifold


Author: Hector Cordova Bulens
Journal: Proc. Amer. Math. Soc. 143 (2015), 5437-5453
MSC (2010): Primary 55P62
DOI: https://doi.org/10.1090/proc/12666
Published electronically: April 14, 2015
MathSciNet review: 3411158
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Abstract: Let $ M$ be a simply connected closed manifold of dimension $ n$. We study the rational homotopy type of the configuration space of two points in $ M$, $ F(M,2)$. When $ M$ is even dimensional, we prove that the rational homotopy type of $ F(M,2)$ depends only on the rational homotopy type of $ M$. When the dimension of $ M$ is odd, for every $ x\in H^{n-2} (M, \mathbb{Q})$, we construct a commutative differential graded algebra $ C(x)$. We prove that for some $ x \in H^{n-2} (M; \mathbb{Q})$, $ C(x)$ encodes completely the rational homotopy type of $ F(M,2)$. For some class of manifolds, we show that we can take $ x=0$.


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Hector Cordova Bulens
Affiliation: Institut de Recherche en Mathémathique et Physique-IRMP; Université caltholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium
Email: hector.cordova@uclouvain.be

DOI: https://doi.org/10.1090/proc/12666
Received by editor(s): February 20, 2014
Received by editor(s) in revised form: October 27, 2014, and October 28, 2014
Published electronically: April 14, 2015
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2015 American Mathematical Society