On the local structure of the SL(n,C)-representation variety of knot groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913708788154368 |
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| author | Heusener, Michael Abdelghani, Leila Ben |
| author_facet | Heusener, Michael Abdelghani, Leila Ben |
| contents | We study the local structure of the representation variety of a knot group into SL(n,C) 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the local structure of the SL(n,C)-representation variety of knot groups Heusener, Michael Abdelghani, Leila Ben Geometric Topology We study the local structure of the representation variety of a knot group into SL(n,C) 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. |
| title | On the local structure of the SL(n,C)-representation variety of knot groups |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2404.09548 |