论文标题
解决两个偏板群的家庭的同构问题
Solving the isomorphism problems for two families of parafree groups
论文作者
论文摘要
对于任何整数$ m，n $带有$ m \ ne 0 $和$ n> 0 $，让$ g_ {m，n} $表示由$ \ langle x，y，y，z \ mid x = [z^m，x] [z^n，y] \ rangle $表示的组;对于任何整数$ m，n> 0 $，令$ h_ {m，n} $表示由$ \ langle x，y，y，z \ mid x = [x^m，z^n] [y，z] \ rangle $。通过调查不可约合$ {\ rm gl}（2，\ mathbb {c}）$ - 角色品种的共同学跳跃基因座，我们显示：如果$ m，m，m'\ ne 0 $，$ n，n'> 0 $ and $ g_ and $ g_ and $ g_ {m'，n'}如果$ m，m'，n，n'> 0 $和$ h_ {m'，n'} \ cong h_ {m，n} $，则$ m'= m，n'= n $。
For any integers $m,n$ with $m\ne 0$ and $n>0$, let $G_{m,n}$ denote the group presented by $\langle x,y,z\mid x=[z^m,x][z^n,y]\rangle$; for any integers $m,n>0$, let $H_{m,n}$ denote the group presented by $\langle x,y,z\mid x=[x^m,z^n][y,z]\rangle$. By investigating cohomology jump loci of irreducible ${\rm GL}(2,\mathbb{C})$-character varieties, we show: if $m,m'\ne 0$, $n,n'>0$ and $G_{m',n'}\cong G_{m,n}$, then $m=m',n=n'$; if $m,m',n,n'>0$ and $H_{m',n'}\cong H_{m,n}$, then $m'=m, n'=n$.
