Deforming abelian elliptic $\mathrm{SL}(2,\mathbb{R})$--representations of knot groups
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915570083954688 |
|---|---|
| author | Liu, Yi |
| author_facet | Liu, Yi |
| contents | The following criterion is proved in this paper. If the Alexander polynomial of a knot $K\subset S^3$ has a zero of odd order on the complex unit circle, then there exists a continuous family of irreducible representations $π_1(S^3\setminus K)\to \mathrm{SL}(2,\mathbb{R})$ converging to an abelian representation of noncentral elliptic type. As an application, the author shows that the Alexander polynomial of any nontrivial L-space knot satisfies the condition of the criterion. In particular, it follows that the fundamental group of any nontrivial L-space knot complement admits an irreducible $\mathrm{SL}(2,\mathbb{R})$--representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deforming abelian elliptic $\mathrm{SL}(2,\mathbb{R})$--representations of knot groups Liu, Yi Geometric Topology Primary 57K31, 57K14, Secondary 12D10 The following criterion is proved in this paper. If the Alexander polynomial of a knot $K\subset S^3$ has a zero of odd order on the complex unit circle, then there exists a continuous family of irreducible representations $π_1(S^3\setminus K)\to \mathrm{SL}(2,\mathbb{R})$ converging to an abelian representation of noncentral elliptic type. As an application, the author shows that the Alexander polynomial of any nontrivial L-space knot satisfies the condition of the criterion. In particular, it follows that the fundamental group of any nontrivial L-space knot complement admits an irreducible $\mathrm{SL}(2,\mathbb{R})$--representation. |
| title | Deforming abelian elliptic $\mathrm{SL}(2,\mathbb{R})$--representations of knot groups |
| topic | Geometric Topology Primary 57K31, 57K14, Secondary 12D10 |
| url | https://arxiv.org/abs/2510.19748 |