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Results tagged with symplectic-topology
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user 424
3
votes
Accepted
On the de Rham cohomology of 1-forms in cotangent bundle.
As has been noted in Peter Michor's answer, a Hamiltonian isotopy can certainly move the graph of a closed one-form to a Lagrangian submanifold that is not the graph of a one-form.
However, in the sp …
- 2,927
4
votes
Accepted
codimension of bubbling of disk and sphere
Moduli spaces of psuedoholomorphic curves have an associated expected dimension, given by the Fredholm index of the appropriate Cauchy-Riemann operator; if an appropriate transversality condition hold …
- 2,927
7
votes
Accepted
Symplectic blow-up
I don't know a place where this is written up explicitly, but it's not hard as soon as one has an appropriate standard model for a neighborhood of a symplectic manifold for use in the Weinstein Neighb …
- 2,927
13
votes
Accepted
Why (and whether) is any smooth embedded torus in R^4 isotopic to an embedded Lagrangian torus?
Whoever told you that any embedded torus in R4 is isotopic to a Lagrangian torus was sorely mistaken. Luttinger (JDG 1995) observed the following: The manifolds obtained by doing certain Dehn-type su …
- 2,927
19
votes
Accepted
Is the Fukaya category "defined"?
From what I understand, the most fundamental issue obstructing the definition of the Fukaya category in general is the fact that the boundaries of the relevant moduli spaces typically have codimension …
- 2,927