Rational model of the configuration space of two points in a simply connected closed manifold
(2015) Proceedings of the American Mathematical Society — Vol. 143, n° 12, p. 5437-5453 (2015)
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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 ofM is odd, for every x ∈ Hn−2(M,Q), we construct a commutative differential graded algebra C(x). We prove that for some x ∈ Hn−2(M;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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Cordova Bulens, H. (2015). Rational model of the configuration space of two points in a simply connected closed manifold. Proceedings of the American Mathematical Society, 143(12), 5437-5453. https://doi.org/10.1090/proc/12666 (Original work published 2015)