Quandle homology and complex volume

Ayumu Inoue; Yuichi Kabaya

Quandle homology and complex volume

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arxiv 1012.2923 v3 pith:WJDHAD5G submitted 2010-12-14 math.GT

Ayumu Inoue , Yuichi Kabaya This is my paper · ORCID

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keywords homologyquandlecomplexgroupsimplicialvolumeapplicationcalled

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We introduce a new homology theory of quandles, called simplicial quandle homology, which is quite different from quandle homology developed by Carter et al. We construct a homomorphism from a quandle homology group to a simplicial quandle homology group. As an application, we obtain a method for computing the complex volume of a hyperbolic link only from its diagram.

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Zesting and the relative complexity of Reshetikhin-Turaev invariants
math.QA 2026-08 conditional novelty 7.0 of 10

Zesting preserves the computational complexity of Reshetikhin-Turaev invariants for links colored by simple objects, via a new polynomial-time computable invariant J_zeta.

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