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Symplectic homology I open sets in ℂ n

Symplectic homology I open sets in ℂ n,10.1007/BF02571699,Mathematische Zeitschrift,A. Floer,H. Hofer

Symplectic homology I open sets in ℂ n   (Citations: 37)
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Journal: Mathematische Zeitschrift - MATH Z , vol. 215, no. 1, pp. 37-88, 1994
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    • ...This information is impossible to be detected by the variational approach and that is the reason, which directs us to work with the Floer-Hofer capacity which is based on the symplectic homology of Floer and Hofer, [11]...
    • ...Originally it was introduced by A. Floer and H. Hofer for bounded, open sets in R 2n , [11], by further developing the idea behind the Floer theory and combining that with ideas of I. Ekeland and H. Hofer about using the Hamiltonian dynamics to study the symplectic rigidity, [7, 8]. Later on versions of the symplectic homology, concerning relatively compact sets in symplectic manifolds with contact type boundary, [4] and symplectic ...
    • ...Here we are going to use the original version of the symplectic homology from [11], with Z2-coefficients, and refer the interested reader to the survey paper of A. Oancea, [20], where the different versions of the symplectic homology are compared...
    • ...In [11], the transversality of the Floer’s equation,(14), is established for a dense subset of Hreg(U) × J. Following the discussion...
    • ...Remark 1. Standard arguments as in [11, 4] show that the monotonicity map, m(H1, H2), is independent of the choice of the monotone homotopy used to define it...

    Dragomir L. Dragnev. Symplectic rigidity, symplectic fixed points, and global perturbations...

    • ...Cieliebak, Floer and Hofer [15, 7] were the first ones to to introduce such ideas into pseudo-holomorphic curve theory (this drew on the insights obtained in previous work, which used a more conventional variational approach)...

    Paul Seidel. A biased view of symplectic cohomology

    • ...∗ (H 1 ; α). (16) Lemma 2.5 ([6, 4]). The monotone homomorphism does not depend on the choice of the monotone homotopy used to define it and...

    Joa Weber. Noncontractible periodic orbits in cotangent bundles and Floer homolog...

    • ...For details and proofs of these results in the general case of Floer homology, see [3], [5] and [17]...
    • ...For proofs of these Lemmas, see [3], [5] and [17]...
    • ...We can then define HF [a,b) (H; α), even when H has degenerate periodic orbits, as HF [a,b) (K; α). For details and proofs, see [2], [3] and [5]...

    Cesar J. Niche. Non-contractible periodic orbits of Hamiltonian flows on twisted cotan...

    • ...We prove that, when the unit normal bundle of M is homologically trivial in degree dim(M) (for example, if codim(M) > dim(M)), a refined version of the Hofer–Zehnder capacity is finite for all open sets close enough to M. We compute this capacity for certain tubular neighborhoods of M by using a squeezing argument in which the algebraic framework of Floer theory is used to detect nontrivial periodic orbits [18, 19, 26]...

    Ely Kerman. Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets...

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