Floer homology in the cotangent bundle of a closed Finsler manifold and noncontractible periodic orbits
نویسندگان
چکیده
منابع مشابه
Noncontractible periodic orbits in cotangent bundles and Floer homology
For every nontrivial free homotopy class α of loops in any closed connected Riemannian manifold, we prove existence of a noncontractible 1periodic orbit for every compactly supported time-dependent Hamiltonian on the open unit cotangent bundle whenever it is sufficiently large over the zero section. The proof shows that the Biran-Polterovich-Salamon capacity is finite for every closed connected...
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Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set, one can define Floer homology and show that it is naturally isomorphic to singular homology of the free loop space. We review the three isomorphisms construc...
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In an earlier paper we have shown that the pair-of-pants product on the Floer homology of the cotangent bundle of an oriented compact manifold Q corresponds to the Chas-Sullivan loop product on the singular homology of the free loop space of Q. We now give chain level constructions of further product structures in Floer homology, corresponding to the cup product on the homology of any path spac...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2020
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/abb190