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2016 String homology, and closed geodesics on manifolds which are elliptic spaces
John Jones, John McCleary
Algebr. Geom. Topol. 16(5): 2677-2690 (2016). DOI: 10.2140/agt.2016.16.2677


Let M be a closed, simply connected, smooth manifold. Let Fp be the finite field with p elements, where p > 0 is a prime integer. Suppose that M is an Fp–elliptic space in the sense of Félix, Halperin and Thomas (1991). We prove that if the cohomology algebra H(M, Fp) cannot be generated (as an algebra) by one element, then any Riemannian metric on M has an infinite number of geometrically distinct closed geodesics. The starting point is a classical theorem of Gromoll and Meyer (1969). The proof uses string homology, in particular the spectral sequence of Cohen, Jones and Yan (2004), the main theorem of McCleary (1987), and the structure theorem for elliptic Hopf algebras over Fp from Félix, Halperin and Thomas (1991).


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John Jones. John McCleary. "String homology, and closed geodesics on manifolds which are elliptic spaces." Algebr. Geom. Topol. 16 (5) 2677 - 2690, 2016.


Received: 11 November 2014; Revised: 17 March 2016; Accepted: 26 March 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1382.55007
MathSciNet: MR3572344
Digital Object Identifier: 10.2140/agt.2016.16.2677

Primary: 55P50
Secondary: 55P35 , 55T05 , 58E10

Keywords: closed geodesics , string homology

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 5 • 2016
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