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Results tagged with sg.symplectic-geometry
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user 10839
Hamiltonian systems, symplectic flows, classical integrable systems
8
votes
Accepted
Applications of Floer homology
Floer homology has, in one form or another, become ubiquitous in symplectic geometry and to give a complete list of its applications would be a mammoth task. Here are a few.
1) One early incarnation …
- 7,005
12
votes
Why believe Kontsevich cosheaf conjecture?
On the suggestion of DamienC, I'm converting my comments into an answer. I didn't do this before because I don't really know the answer to the deeper question of why the microlocal sheaf category is t …
- 7,005
5
votes
Accepted
Progress on composition of Lagrangian correspondences/definition of symplectic categories?
Though not about solving the nontransversality problem, Fukaya's paper Unobstructed immersed Lagrangian correspondence and filtered A infinity functor is the state of the art in why nontransversality …
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4
votes
When do you go hunting for Lagrangian submanifolds?
One goes hunting for Lagrangian submanifolds if one is interested in defining gauge theoretic 3-manifold invariants by cutting along a Heegaard surface.
Lagrangian submanifolds arise in gauge theory …
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4
votes
When do you go hunting for Lagrangian submanifolds?
Another place where Lagrangian submanifolds arise naturally is in cotangent bundles. If $M\subset N$ is a submanifold then you can define the conormal bundle of $M$ to be the set of covectors which an …
- 7,005
3
votes
Accepted
Isotrivial Monodromy
I think the answer is yes, depending on how you are defining the monodromy*. I take "isotrivial" to mean that you have a smooth fibre bundle over the punctured plane where the fibres have complex stru …
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2
votes
Clarification on the ”neck stretching” applied to the base space of a Lefschetz fibration
For a start, the base of your Lefschetz fibration had better be
a Riemann surface, or else it won't have any pseudoholomorphic sections for
generic J (see for example Kruglikov's paper https://link.sp …
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0
votes
The higher structure of the Floer cochains of the diagonal in CP^ x CP^n
I was browsing old symplectic questions and spotted this one. I realise that in the intervening decade you "learned a little Lagrangian Floer theory" like the question says, but maybe you'll enjoy ano …
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1
vote
Strictly isotropic and strictly coisotropic submanifolds
I must be getting conservative in my old age: I'd advise against coining new terminology unless it makes your paper substantially more readable. Definitely "subcritical" (and possibly "supercritical") …
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4
votes
Accepted
$\mathbb{R}\mathbb{P}^n$ is monotone in $\mathbb{C}\mathbb{P}^n$, Lagrangian floer cohomology
The relative homology long exact sequence puts this group in between $H_2(\mathbb{CP}^n)=\mathbb{Z}$ and $\mathbb{Z}/2$. It maps surjectively to $\mathbb{Z}/2$. Let D be a generator for relative homol …
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5
votes
Accepted
Almost toric mutations
Mutation doesn't even change the integral affine base, which is why it doesn't change the symplectic manifold. All you're doing is changing the way the integral affine base is drawn. If you're given a …
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2
votes
Accepted
Could this be a Hamiltonian symplectomorphism on a symplectic toric manifold
Sometimes it is, sometimes it isn't.
The spheres living over the edges generate the second homology, so you can read off the action on $H_2$ from that. For $S^2\times S^2$ (square) the action on homol …
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1
vote
Why are symplectic toric varieties projective?
Not a full answer, but a partial answer to your question 1a.
Torus-invariant Kaehler metrics (in particular complex structures) were constructed by Guillemin, just starting with data on the moment pol …
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21
votes
Why are Gromov-Witten invariants of K3 surfaces trivial?
Here are two answers to your first question:
Yes your argument works. To see that there are no curves for a generic K3 observe that their homology classes must be Poincare dual to an integral (1,1)- …
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4
votes
Computation of Gromov-Witten invariants for symplectic manifolds
I noticed this question a few weeks ago but waited to post an answer before I could say: here's a new computation (http://arxiv.org/abs/1106.3959) for a class of non-Kaehler manifolds.
Psychologicall …
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