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On the local
structure of the $\mathrm{SL}(n,\mathbb{C})$ representation
variety of knot groups
Leila Ben Abdelghani and Michael Heusener |
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Vol. 8 (2026), No. 1, 1–40
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Abstract |
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We study the local structure of the representation variety of a knot group into the special linear group of degree over the complex numbers at certain diagonal representations. In particular we determine the tangent cone of the representation variety at these diagonal representations, and show that the latter can be deformed into irreducible representations. Furthermore, we use Luna’s slice theorem to analyze the local structure of the character variety. |
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Keywords
knot group, variety of representations, deformations of
reducible representations
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Mathematical Subject Classification
Primary: 57K31
Secondary: 20C99, 57M05
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Milestones
Received: 20 July 2024
Revised: 25 January 2025
Accepted: 9 February 2025
Published: 13 January 2026
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Authors |
| Leila Ben Abdelghani | |
| Département de Mathématiques Faculté des Sciences Université de Monastir Monastir Tunisia |
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| Michael Heusener | |
| Laboratoire de Mathématiques Blaise
Pascal - UMR 6620 - CNRS Université Clermont Auvergne Aubière France |
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| © 2026 MSP (Mathematical Sciences Publishers). |
