一族两个生成元的非霍普夫群
A family of two generator non-Hopfian groups
摘要：
我们构造了$2$生成元非霍普夫群$G_m, m=3, 4, 5, \dots$，其中每个$G_m$都有一个特定的表示$G_m=\langle a, b \, | \, u_{r_{m,0}}=u_{r_{m,1}}=u_{r_{m,2}}= \cdots =1 \rangle$，它满足小消去条件$C(4)$和$T(4)$ .这里，$u_{r_{m,i}}$是$2$的上表示的单个关系子-斜率$r_{m,i}$的桥连接组，其中$r_{m,0}=[m+1,m,m]$和$r_{m,i}=[m+1,m-1,(i-1)\langle m \rangle,m+1,m]$在连分数展开中对于每个整数$i \ge 1$。
英文摘要：
We construct $2$-generator non-Hopfian groups $G_m, m=3, 4, 5, \dots$, where each $G_m$ has a specific presentation $G_m=\langle a, b \, | \, u_{r_{m,0}}=u_{r_{m,1}}=u_{r_{m,2}}= \cdots =1 \rangle$ which satisfies small cancellation conditions $C(4)$ and $T(4)$. Here, $u_{r_{m,i}}$ is the single relator of the upper presentation of the $2$-bridge link group of slope $r_{m,i}$, where $r_{m,0}=[m+1,m,m]$ and $r_{m,i}=[m+1,m-1,(i-1)\langle m \rangle,m+1,m]$ in continued fraction expansion for every integer $i \ge 1$.
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