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The homology of a
free loop space
Stephen Halperin and Micheline Vigué |
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Vol. 147 (1991), No. 2, 311–324
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Abstract |
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Denote by XS1 the space of all continuous maps from the circle into a simply connected finite CW complex, X. Theorem: Let k be a field and suppose that either chark > dimX or that X is k-formal. Then the betti numbers bq = dimHq(XS1 ;k) are uniformly bounded above if and only if the k-algebra H∗(X;k) is generated by a single cohomology class. Corollary: If, in addition, X is a smooth closed manifold and k is as in the theorem, and if H∗(X;k) is not generated by a single class then X has infinitely many distinct closed geodesics in any Riemannian metric. |
Mathematical Subject Classification 2000
Primary: 55P99
Secondary: 55N99, 55T99, 57R19
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Milestones
Received: 6 March 1989
Published: 1 February 1991
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Authors |
| Stephen Halperin | |
| Micheline Vigué | |
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