There's an excercise problem in Heckman's symplectic geometry book that says $\mathbb{S}^n$ is a symplectic manifold iff $n=0$ or $n=2$, but I don't see the structure over $\mathbb{S}^0$.
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4$\mathbb{S}^0$ is two isolated points, whose tangent bundles are 0-dimensional. Any 0-dimensional space has a unique symplectic structure (the zero bilinear form). Having said that it seems like a silly special case. – Joppy Oct 06 '20 at 03:14
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You're absolutely right. Thanks – Gyadso Oct 06 '20 at 03:29
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Here's a curiosity about the existence of symplectic forms in products of spheres. – Ivo Terek Oct 06 '20 at 04:22