论文标题
蛋白2和3属的符号表面上的鸡蛋动力学
Eggbeater dynamics on symplectic surfaces of genus 2 and 3
论文作者
论文摘要
符合歧管$（m，ω）$的所有哈密顿二差异性的$ ham（m，ω）$在符号几何形状中起着核心作用。该组具有HOFER指标。在本文中，我们研究了$ ham（m，ω）$的几何形状的两个方面，如果$ m $是第2属或3属的封闭式表面。首先，我们证明，$ ham（m，ω）$在$ k $ the $ k $ the the the $ k $ the the $ k $ the the $ k $ k geq for notric中，对任何$ k k $ k geq ceq 2 $ \ geq 2 $。该部分概括了Polterovich和Shelukhin的先前工作。其次，我们表明两个发电机上的自由组嵌入$ ham（m，ω）$的渐近锥中。该部分扩展了Alvarez-Gavela等人的先前工作。这两种扩展都基于几何群体理论的两个结果，这些结果涉及表面嵌入的不可压缩性。
The group $Ham(M,ω)$ of all Hamiltonian diffeomorphisms of a symplectic manifold $(M,ω)$ plays a central role in symplectic geometry. This group is endowed with the Hofer metric. In this paper we study two aspects of the geometry of $Ham(M,ω)$, in the case where $M$ is a closed surface of genus 2 or 3. First, we prove that there exist diffeomorphisms in $Ham(M,ω)$ arbitrarily far from being a $k$-th power, with respect to the metric, for any $k \geq 2$. This part generalizes previous work by Polterovich and Shelukhin. Second, we show that the free group on two generators embeds into the asymptotic cone of $Ham(M,ω)$. This part extends previous work by Alvarez-Gavela et al. Both extensions are based on two results from geometric group theory regarding incompressibility of surface embeddings.
