Multiplicity of non-acyclic ${\rm SL}_2$-representations and L-functions of the odd-twisted Whitehead links
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| Format: | Preprint |
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2023
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| _version_ | 1866913025446903808 |
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| author | Bénard, Léo Tange, Ryoto Tran, Anh T. Ueki, Jun |
| author_facet | Bénard, Léo Tange, Ryoto Tran, Anh T. Ueki, Jun |
| contents | We study the divisor of the Reidemeister torsion on the variety of irreducible ${\rm SL}_2\mathbb{C}$-characters of certain knots and links, and provide a geometric interpretation of them. We focus in particular on the family of odd-twisted Whitehead links $W_{2n-1}$ and prove that these divisors have multiplicity two. Furthermore, we apply these results to the study of the $L$-functions of the universal deformations of representations over fields with characteristic $p>2$ of these link groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_15941 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multiplicity of non-acyclic ${\rm SL}_2$-representations and L-functions of the odd-twisted Whitehead links Bénard, Léo Tange, Ryoto Tran, Anh T. Ueki, Jun Geometric Topology Number Theory Primary 57K10, 11R23, Secondary 57K31, 11S05 We study the divisor of the Reidemeister torsion on the variety of irreducible ${\rm SL}_2\mathbb{C}$-characters of certain knots and links, and provide a geometric interpretation of them. We focus in particular on the family of odd-twisted Whitehead links $W_{2n-1}$ and prove that these divisors have multiplicity two. Furthermore, we apply these results to the study of the $L$-functions of the universal deformations of representations over fields with characteristic $p>2$ of these link groups. |
| title | Multiplicity of non-acyclic ${\rm SL}_2$-representations and L-functions of the odd-twisted Whitehead links |
| topic | Geometric Topology Number Theory Primary 57K10, 11R23, Secondary 57K31, 11S05 |
| url | https://arxiv.org/abs/2303.15941 |