A relation between the Baseilhac-Benedetti and the Bonahon-Liu-Wong-Yang invariants
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| Format: | Preprint |
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2026
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| _version_ | 1866908750936276992 |
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| author | Garoufalidis, Stavros Yu, Tao |
| author_facet | Garoufalidis, Stavros Yu, Tao |
| contents | Baseilhac-Benedetti, following ideas of Kashaev, introduced invariants of pseudo-Anosov homeomorphisms of punctured hyperbolic surfaces that depend on a complex root of unity of odd order. Around the same time, Bonahon-Liu introduced another set of invariants of pseudo-Anosov homeomorphisms at roots of unity. A little later, Dimofte and the first author introduced invariants of cusped hyperbolic 3-manifolds at roots of unity using their geometric representation. In another effort, Bonahon-Wong-Yang introduced another set of invariants of pseudo-Anosov homeomorphisms at roots of unity. All these invariants are conjecturally closely related, and our aim is to prove a precise relation between the Baseilhac-Benedetti invariants, the Bonahon-Liu-Wong-Yang and the lesser-known abelian $\mathfrak{gl}_1$-invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03554 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A relation between the Baseilhac-Benedetti and the Bonahon-Liu-Wong-Yang invariants Garoufalidis, Stavros Yu, Tao Geometric Topology Baseilhac-Benedetti, following ideas of Kashaev, introduced invariants of pseudo-Anosov homeomorphisms of punctured hyperbolic surfaces that depend on a complex root of unity of odd order. Around the same time, Bonahon-Liu introduced another set of invariants of pseudo-Anosov homeomorphisms at roots of unity. A little later, Dimofte and the first author introduced invariants of cusped hyperbolic 3-manifolds at roots of unity using their geometric representation. In another effort, Bonahon-Wong-Yang introduced another set of invariants of pseudo-Anosov homeomorphisms at roots of unity. All these invariants are conjecturally closely related, and our aim is to prove a precise relation between the Baseilhac-Benedetti invariants, the Bonahon-Liu-Wong-Yang and the lesser-known abelian $\mathfrak{gl}_1$-invariants. |
| title | A relation between the Baseilhac-Benedetti and the Bonahon-Liu-Wong-Yang invariants |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2601.03554 |