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Hamiltonian systems, symplectic flows, classical integrable systems

15 votes
3 answers
2k views

Unstable manifolds of a Morse function give a CW complex

A coauthor of mine and I want to use the following innocent looking statement in a forthcoming paper: Statement. Let M2n be a compact manifold and let f be a Morse function with critical point …
Dmitri Panov's user avatar
  • 28.9k
17 votes
1 answer
905 views

Finite fundamental groups of 3-dimensional Calabi-Yau manifolds

Question. Is there an example of a compact 3-dimensional Calabi-Yau manifold with finite fundamental group G that does not admit a free action on S3? This question is motivated by the followin …
Dmitri Panov's user avatar
  • 28.9k
24 votes
3 answers
1k views

Hyperbolic Coxeter polytopes and Del-Pezzo surfaces

Added. In the following link there is a proof of the observation made in this question: http://dl.dropbox.com/u/5546138/DelpezzoCoxeter.pdf I would like to find a reference for a beautiful construc …
Dmitri Panov's user avatar
  • 28.9k
8 votes
1 answer
630 views

Are there symplectic 4-folds with b+>1, b=0?

This is the question. Is it known that a symplectic 4-fold with b2>1 should have a homology class C with C2<0?
Dmitri Panov's user avatar
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12 votes
0 answers
849 views

Compact Symplectic Fano (strongly monotone) manfiolds

What are known examples of compact symplectic Fano manifolds, apart from those that come from algebraic geometry? We define symplectic Fano manifold as a symplectic manifold (M,w), such that $[c_1 …
Dmitri Panov's user avatar
  • 28.9k
10 votes
3 answers
1k views

Hamiltonian S1 actions with isolated fixed points

I have in mind the following question for some time. Is there an example of a compact symplectic manifold with a Hamiltonian S1-action with isolated fixed points, that does not admit a compatible $ …
26 votes
2 answers
2k views

Manifolds distinguished by Gromov-Witten invariants?

What is a simplest example of a manifold M2n that admits two symplectic structures with isotopic almost complex structures, and such that Gromov-Witten invariants of these symplectic structures …
Dmitri Panov's user avatar
  • 28.9k