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Estimates for the Betti Numbers of Rationally Elliptic Spaces

✍ Scribed by A. V. Pavlov

Book ID
110404812
Publisher
SP MAIK Nauka/Interperiodica
Year
2002
Tongue
English
Weight
168 KB
Volume
43
Category
Article
ISSN
0037-4466

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We compute the rational Betti numbers of the configuration space C k (M) of k points in an evendimensional 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-PoincarΓ© characteristic of C k (M)

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Let X be a simply connected ΓΏnite CW-complex such that dim \* (X ) βŠ— Q = ∞. We prove that if X is coformal (this is an hypothesis coming from the rational homotopy theory) then the sequence of rational Betti numbers of its free loop space, (dim Hn(X S 1 ; Q)) nβ‰₯1 , has an exponential growth. Since t