论文标题
关于订购的编织小组的评论
Remark on ordered braid groups
论文作者
论文摘要
我们从tracial $ c^*$ - algebra $ \ mathbb {a}（s_ {g，n}）$与表面$ s_ {g，n} $相关联的tracuster $ c^*$ - algebra $ \ mathbb {a} $ c^*$ - algebra $ - algebra $ \ algebra $ c^*$ - algebra $ c^*$ - algebra $ c^*$ -s {g，n} $ n $ n $ n $ n $ n $ n $ n $ n $ n。事实证明，基本组$π_1（s_ {g，n}）$的左顺序空间是一个完全断开连接的密度密集的子空间。特别是，$π_1（s_ {g，n}）$的每个左顺序都定义了在空间$ t_ {g，n} $的地理流量下的Riemann Surface $ S_ {G，N} $的轨道。
We recover the Dehornoy order on the braid group $B_{2g+n}$ from the tracial state on a cluster $C^*$-algebra $\mathbb{A}(S_{g,n})$ associated to the surface $S_{g,n}$ of genus $g$ with $n$ boundary components. It is proved that the space of left-ordering of the fundamental group $π_1(S_{g,n})$ is a totally disconnected dense subspace of the projective Teichmüller space $\mathbb{P}T_{g,n}\cong \mathbf{R}^{6g-7+2n}$. In particular, each left-ordering of $π_1(S_{g,n})$ defines the orbit of a Riemann surface $S_{g,n}$ under the geodesic flow on the space $T_{g,n}$.
