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Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.

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Existence of a symplectic form in a given class for the product of Riemann surfaces

Let $a \in H^2(M, \mathbb{R})$ be a cohomology class of a closed manifold $M$ of dimension $2n$. For the cohomology class $a$ to represent a symplectic form on $M$, we must have $a^n \neq 0$. This is …