Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2009.01412 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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 $m'=m, n'=n$.