Rational model of the configuration space of two points in a simply connected closed manifold
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- by Hector Cordova Bulens PDF
- Proc. Amer. Math. Soc. 143 (2015), 5437-5453 Request permission
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 $x=0$.References
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Additional Information
- 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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 5437-5453
- MSC (2010): Primary 55P62
- DOI: https://doi.org/10.1090/proc/12666
- MathSciNet review: 3411158