Search arXivSearch

arXiv · math/0009165

On the volume conjecture for hyperbolic knots

Abstract

In this article, we give a rough, and so not complete yet, proof of Kashaev's conjecture, that is, the volume conjecture for hyperbolic knots, where the hyperbolicity equations associated to knot diagrams appear as the stationary phase equations for Kashaev's invariants.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yoshiyuki Yokota. 2000-09-18. On the volume conjecture for hyperbolic knots. https://arxiv.org/abs/math/0009165

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Categorification of quasi-split iquantum groups

We introduce a new family of graded 2-categories generalizing the 2-quantum groups introduced by Khovanov, Lauda and Rouquier. We use them to categorify quasi-split iquantum groups in all symmetric types.

math.QA

The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid

In a previous article, we showed that local projectivity is a sufficient condition for the existence of a bialgebroid structure on the ring of differential operators on an affine variety. In this note, we show using elementary methods that the ring of differential operators on a nodal curve is neither locally projective nor does it admit a bialgebroid structure.

math.QA

Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction

We give complete conjugacy classes of modular group SL(2,Z). Particularly, the conjugacy classes of hyperbolic elements are decided by the proper equivalence classes of indefinite forms, and we give an example. Finally, we describe the coset representatives of centralizer of S, ST, T and hyperbolic elements of SL(2,Z) by regular continued fraction. In conclusion, most Nichols algebras over modular group are infinite-dimensional except Proposition 4.10.

math.QA