Quandle homology and complex volume

Abstract

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.

27 pages, 11 figures; added Lemma 7.2

References in corpus (2)

• Twisted quandle homology theory and cocycle knot invariants
• A dilogarithmic formula for the Cheeger-Chern-Simons class

Cited by in corpus (2)

• Cyclic branched coverings of knots and quandle homology
• On third homologies of groups and of quandles via the Dijkgraaf-Witten invariant and Inoue-Kabaya map