Symplectic, Poisson, and contact geometry on scattering manifolds
Symplectic, Poisson, and contact geometry on scattering manifolds
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散射流形上的辛几何、泊松几何和接触几何
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发表时间：
2016
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通讯作者：
Melinda Lanius
中科院分区：
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作者：
Melinda Lanius
我们引入散射辛流形，流形的一种最小退化泊松结构，是不是太严格，以便有一个大类的例子，但限制足够的标准泊松不变量是可计算的。本文将证明散射辛设置的潜力。特别地，我们构造了接触流形的强凸辛填充之间的散射辛球和散射辛胶接。通过给出散射辛流形的Poisson上同调的一个显式计算，引入了一种计算Poisson上同调的新方法，并将其应用于$B^k$-辛流形。
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplectic setting. In particular, we construct scattering-symplectic spheres and scattering symplectic gluings between strong convex symplectic fillings of a contact manifold. By giving an explicit computation of the Poisson cohomology of a scattering symplectic manifold, we introduce a new method of computing Poisson cohomology and apply it to $b^k$-symplectic manifolds.