论文标题
在泊松结构空间上的泊松支架
A Poisson bracket on the space of Poisson structures
论文作者
论文摘要
令$ m $为平滑的封闭式定向歧管，$ \ Mathcal {p}（m）$ $ m $上的泊松结构的空间。我们在$ \ mathcal {p}（m）$上构建泊松支架，具体取决于音量表单的选择。括号的哈密顿流动作用于$ \ mathcal {p}（m）$ $ $ m $ $ m $。然后，我们定义了一个泊松结构的不变性，该结构描述了流程方程的固定点，并为常规泊松3个manifolds计算它，在该泊松中检测到单峰性。对于单模型的泊松结构，我们定义了一个相关的泊松支架，并表明，对于符号结构，流动方程的相关计数固定点是根据tseng和yau定义的$ d d^λ$和$ d d^λ$和$ d+ d+ d^λ$ symplectic coomplectic colomology组的。
Let $M$ be a smooth closed orientable manifold and $\mathcal{P}(M)$ the space of Poisson structures on $M$. We construct a Poisson bracket on $\mathcal{P}(M)$ depending on a choice of volume form. The Hamiltonian flow of the bracket acts on $\mathcal{P}(M)$ by volume-preserving diffeomorphism of $M$. We then define an invariant of a Poisson structure that describes fixed points of the flow equation and compute it for regular Poisson 3-manifolds, where it detects unimodularity. For unimodular Poisson structures we define a further, related Poisson bracket and show that for symplectic structures the associated invariant counting fixed points of the flow equation is given in terms of the $d d^Λ$ and $d+ d^Λ$ symplectic cohomology groups defined by Tseng and Yau.
