Character varieties of torus links
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914685161308160 |
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| author | González-Prieto, Ángel Martínez, Javier Muñoz, Vicente |
| author_facet | González-Prieto, Ángel Martínez, Javier Muñoz, Vicente |
| contents | In this paper, we study the geometry of the moduli space of representations of the fundamental group of the complement of a torus link into an algebraic group G, an algebraic variety known as the G-character variety of the torus link. These torus links are a family of links in the 3-dimensional sphere formed by stacking several copies of torus knots. We develop an intrinsic stratification of the variety that allows us to relate its geometry with the one of the underlying torus knot. Using this information, we explicitly compute the E-polynomial associated to the Hodge structure of these varieties for $G=SL_2(\mathbb{C})$ and $SL_3(\mathbb{C})$, for an arbitrary torus link, showing an unexpected relation with the number of strands of the link. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12286 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Character varieties of torus links González-Prieto, Ángel Martínez, Javier Muñoz, Vicente Geometric Topology 57K31, 14D20, 14C30 In this paper, we study the geometry of the moduli space of representations of the fundamental group of the complement of a torus link into an algebraic group G, an algebraic variety known as the G-character variety of the torus link. These torus links are a family of links in the 3-dimensional sphere formed by stacking several copies of torus knots. We develop an intrinsic stratification of the variety that allows us to relate its geometry with the one of the underlying torus knot. Using this information, we explicitly compute the E-polynomial associated to the Hodge structure of these varieties for $G=SL_2(\mathbb{C})$ and $SL_3(\mathbb{C})$, for an arbitrary torus link, showing an unexpected relation with the number of strands of the link. |
| title | Character varieties of torus links |
| topic | Geometric Topology 57K31, 14D20, 14C30 |
| url | https://arxiv.org/abs/2402.12286 |