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This is the question. Is it known that a symplectic $4$-fold with $b_2>1$ should have a homology class $C$ with $C^2<0$?

What is a simplest example of a manifold $M^{2n}$ that admits two symplectic structures with isotopic almost complex structures, and such that Gromov-Witten invariants of these symplectic structures …

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 …

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 $S^3$? This question is motivated by the followin …

A coauthor of mine and I want to use the following innocent looking statement in a forthcoming paper: Statement. Let $M^{2n}$ be a compact manifold and let $f$ be a Morse function with critical point …

I have in mind the following question for some time. Is there an example of a compact symplectic manifold with a Hamiltonian $S^1$-action with isolated fixed points, that does not admit a compatible $ …

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 …