拟态射到圆盘的辛态射群的扩张
Extensions of quasi-morphisms to the symplectomorphism group of the disk
摘要：
在圆盘的在边界附近为单位元的辛态射群$\rm{Symp}(D, \partial D)$上，存在称为Ruelle不变量的齐次拟态射和Gambaudo-Ghys拟态射.在本文中，我们证明了上述齐次拟态射推广到整个圆盘的辛态射群$\rm{Symp}(D)$上的齐次拟态射。作为推论，我们证明了第二有界上同调$H_b^2(\rm{Symp}(D))$是无穷维的。
英文摘要：
On the group $\rm{Symp}(D, \partial D)$ of symplectomorphisms of the disk which are the identity near the boundary, there are homogeneous quasi-morphisms called the Ruelle invariant and Gambaudo-Ghys quasi-morphisms. In this paper, we show that the above homogeneous quasi-morphisms extend to homogeneous quasi-morphisms on the whole group $\rm{Symp}(D)$ of symplectomorphisms of the disk. As a corollary, we show that the second bounded cohomology $H_b^2(\rm{Symp}(D))$ is infinite-dimensional.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
