Kashaev invariants of twice-iterated torus knots

Hitoshi Murakami; Anh T. Tran

doi:10.1016/j.topol.2021.107602

Kashaev invariants of twice-iterated torus knots

Hitoshi Murakami, Anh T. Tran

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We calculate the asymptotic behavior of the Kashaev invariant of a twice-itarated torus knot and obtain topological interpretation of the formula in terms of the Chern–Simons invariant and the twisted Reidemeister torsion.

Original language	English
Article number	107602
Journal	Topology and its Applications
Volume	290
DOIs	https://doi.org/10.1016/j.topol.2021.107602
Publication status	Published - 2021 Mar 1

Keywords

Chern–Simons invariant
Colored Jones polynomial
Iterated torus knot
Kashaev invariant
Reidemeister torsion
Volume conjecture

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2021.107602

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title = "Kashaev invariants of twice-iterated torus knots",

abstract = "We calculate the asymptotic behavior of the Kashaev invariant of a twice-itarated torus knot and obtain topological interpretation of the formula in terms of the Chern–Simons invariant and the twisted Reidemeister torsion.",

keywords = "Chern–Simons invariant, Colored Jones polynomial, Iterated torus knot, Kashaev invariant, Reidemeister torsion, Volume conjecture",

author = "Hitoshi Murakami and Tran, {Anh T.}",

note = "Funding Information: H.M. was supported by JSPS KAKENHI Grant Numbers 26400079 , 17K05239 . A.T. has been partially supported by a grant from the Simons Foundation (# 354595 to AT). Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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AU - Tran, Anh T.

N1 - Funding Information: H.M. was supported by JSPS KAKENHI Grant Numbers 26400079 , 17K05239 . A.T. has been partially supported by a grant from the Simons Foundation (# 354595 to AT). Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - We calculate the asymptotic behavior of the Kashaev invariant of a twice-itarated torus knot and obtain topological interpretation of the formula in terms of the Chern–Simons invariant and the twisted Reidemeister torsion.

AB - We calculate the asymptotic behavior of the Kashaev invariant of a twice-itarated torus knot and obtain topological interpretation of the formula in terms of the Chern–Simons invariant and the twisted Reidemeister torsion.

KW - Chern–Simons invariant

KW - Colored Jones polynomial

KW - Iterated torus knot

KW - Kashaev invariant

KW - Reidemeister torsion

KW - Volume conjecture

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JO - Topology and its Applications

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ER -

Kashaev invariants of twice-iterated torus knots

Abstract

Keywords

ASJC Scopus subject areas

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