A relation between the Baseilhac-Benedetti and the Bonahon-Liu-Wong-Yang invariants

Fuente: arXiv
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Main Authors: Garoufalidis, Stavros, Yu, Tao
Format: Preprint
Published: 2026
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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