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15 June 2006 Noncontractible periodic orbits in cotangent bundles and Floer homology
Joa Weber
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Duke Math. J. 133(3): 527-568 (15 June 2006). DOI: 10.1215/S0012-7094-06-13334-3

Abstract

Let M be a closed connected Riemannian manifold, and let α be a homotopy class of free loops in M. Then, for every compactly supported time-dependent Hamiltonian on the open unit disk cotangent bundle which is sufficiently large over the zero section, we prove the existence of a 1-periodic orbit whose projection to M represents α. The proof shows that the Biran-Polterovich-Salamon capacity of the open unit disk cotangent bundle relative to the zero section is finite. If M is not simply connected, this leads to an existence result for noncontractible periodic orbits on level hypersurfaces corresponding to a dense set of values of any proper Hamiltonian on T*M bounded from below, whenever the levels enclose M. This implies a version of the Weinstein conjecture including multiplicities; we prove existence of closed characteristics—one associated to each nontrivial α—on every contact-type hypersurface in T*M enclosing M

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Joa Weber. "Noncontractible periodic orbits in cotangent bundles and Floer homology." Duke Math. J. 133 (3) 527 - 568, 15 June 2006. https://doi.org/10.1215/S0012-7094-06-13334-3

Information

Published: 15 June 2006
First available in Project Euclid: 13 June 2006

zbMATH: 1120.53053
MathSciNet: MR2228462
Digital Object Identifier: 10.1215/S0012-7094-06-13334-3

Subjects:
Primary: 70H12
Secondary: 37J45 , 53D40

Rights: Copyright © 2006 Duke University Press

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Vol.133 • No. 3 • 15 June 2006
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