论文标题
泊松结构紧凑
Poisson structures with compact support
论文作者
论文摘要
我们明确地构建了具有紧凑支持的几个泊松结构。例如，我们表明，$ \ r^n $上的任何泊松结构最多都可以在开放的球外进行多项式系数，从而得到紧凑的支撑。我们还表明，具有接触或固定边界的符号歧管接收到一个泊松结构，该结构消失在边界处的无限顺序，并同意边界任意小管面外的原始符号结构。结果，我们证明，任何均值的歧管都承认了一个泊松结构，该结构是在一个子集之外是在一个子集之外的象征性的。
We explicitly construct several Poisson structures with compact support. For example, we show that any Poisson structure on $\R^n$ with polynomial coefficients of degree at most two can be modified outside an open ball, such that it becomes compactly supported. We also show that a symplectic manifold with either contact or cosymplectic boundary admits a Poisson structure which vanishes to infinite order at the boundary and agrees with the original symplectic structure outside an arbitrarily small tubular neighbourhood of the boundary. As a consequence, we prove that any even-dimensional manifold admits a Poisson structure which is symplectic outside a codimension one subset.
