Rational Betti numbers of configuration spaces

Félix, Yves;Thomas, JC.
(2000) Topology and Its Applications : a journal devoted to general, geometric, set-theoretic and algebraic topology — Vol. 102, n° 2, p. 139-149 (2000)

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  • Félix, YvesUCLouvain
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  • Thomas, JC.
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Abstract
We compute the rational Betti numbers of the configuration space C-k(M) of k points in an even-dimensional orientable closed manifold M and prove that these numbers depend only on the rational cohomology algebra of the manifold. We give also a formula for the Euler-Poincare characteristic of C-k(M) in terms only of k, and of the Euler-Poincare characteristic of M. (C) 2000 Elsevier Science B.V. All rights reserved.
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Félix, Y., & Thomas, JC. (2000). Rational Betti numbers of configuration spaces. Topology and Its Applications : a journal devoted to general, geometric, set-theoretic and algebraic topology, 102(2), 139-149. https://doi.org/10.1016/S0166-8641(98)00148-5 (Original work published 2000)