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Results tagged with sg.symplectic-geometry
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user 134697
Hamiltonian systems, symplectic flows, classical integrable systems
5
votes
Accepted
Choice of a family of almost complex structures when defining Floer Homology
For a lot of things, you can work with a generic time-independent $J_0$ as you suggest; for instance, Audien & Damien work in this context in their book (so for most of the "fundamental" constructions …
1
vote
Accepted
Generic choice of non-degenerate Hamiltonians $H$ in Floer theory
You can find a statement (and proof) of such a theorem in Hofer-Salamon's Floer homology and Novikov rings, where it appears as Theorem $3.1$. They require also that no holomorphic spheres with first …
2
votes
Linearization of the Floer equation
$\mathcal{F}^{H,J}_u$ is exactly the Floer operator (what you have called $\mathcal{F}$ in your post) locally near the cylinder $u$ in $\mathcal{P}^{1,p}(x^-,x^+)$, after we use the underlying metric …
1
vote
Symplectic vector fields everywhere transverse to a co-dimension one hypersurface
This is a great question! (Or rather, I quite liked it. Reasonable people can differ on this, I suppose.) In fact, local considerations (or even semi-local considerations like understanding the symple …