论文标题
纯辫子组作为区域保护同构的不可证实性
Non-realizability of the pure braid group as area-preserving homeomorphisms
论文作者
论文摘要
令$ \ text {homeo} _+（d^2_n）$为$ d^2 $的方向预示同型同构的组，将边界定位为一组，标记点为一组。 Nielsen实现辫子组的实现问题询问自然投影$ p_n：\ text {homeo} _+（d^2_n）\ to b_n：=π_0（\ text {homeo} _+（d^2_n））$具有$ b_n $的子级别的部分。所有以前的方法都使用扭转或瑟斯顿稳定性，这些稳定性不适用于纯编织组$ pb_n $，$ b_n $的子组固定了$ n $标记点。在本文中，我们表明，纯编织组使用旋转数字在区域保存同构内没有实现。
Let $\text{Homeo}_+(D^2_n)$ be the group of orientation-preserving homeomorphisms of $D^2$ fixing the boundary pointwise and $n$ marked points as a set. Nielsen realization problem for the braid group asks whether the natural projection $p_n:\text{Homeo}_+(D^2_n)\to B_n:=π_0(\text{Homeo}_+(D^2_n))$ has a section over subgroups of $B_n$. All of the previous methods either use torsions or Thurston stability, which do not apply to the pure braid group $PB_n$, the subgroup of $B_n$ that fixes $n$ marked points pointwise. In this paper, we show that the pure braid group has no realization inside the area-preserving homeomorphisms using rotation numbers.
