科研之友
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摘要
A Poisson manifold (M-2n, pi) is b-symplectic if boolean AND(n) pi is transverse to the zero section. We prove an h-principle for open, b-symplectic manifolds, which shows that an open, orientable manifold M is b-symplectic if and only if M x C has an almost-complex structure. For closed, oriented manifolds, we observe that a cosymplectic manifold is the singular locus of a b-symplectic manifold if and only if it is symplectically fillable. We use this observation to prove that every 3-dimensional, closed, orientable cosymplectic manifold is the singular locus of a closed, orientable 4-manifold. We also discuss extensions of this result to higher dimensions.
- 出版日期2017
