## Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces.(English)Zbl 1158.53067

Let $$H$$ be a Hamiltonian on a symplectic manifold $$(W,\omega)$$. One of the most important assumptions in the Floer homology is that the $$1$$-periodic orbits of the Hamiltonian vector field $$X_ H$$ are non-degenerate, which makes $$H$$ time-dependent.
In this paper, the authors generalize the notion of Floer homology by defining it for a time-independent or autonomous Hamiltonian $$H: W\to \mathbb R$$ under the assumption that its $$1$$-periodic orbits are transversally non-degenerate. There is a natural class of time-independent Hamiltonians on $$W$$ whose non-constant $$1$$-periodic orbits correspond precisely to closed Reeb orbits on $$M= \partial W$$ and for which the Floer trajectories can be related to holomorphic cylinders in the symplectization $$M\times\mathbb R$$. The authors relate the Floer trajectories of a specific time-dependent perturbation to the Floer trajectories of the unperturbed Hamiltonian in the way that Floer homology for time-independent Hamiltonians serves as a bridge between symplectic homology and linearized contact homology.

### MSC:

 53D40 Symplectic aspects of Floer homology and cohomology
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### References:

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