A VOLUME PRESENTATION OF A FIBERED KNOT

Hiroshi Goda; Takayuki Morifuji

doi:10.2748/tmj.20230208

A VOLUME PRESENTATION OF A FIBERED KNOT

Hiroshi Goda
, Takayuki Morifuji

経済学部

研究成果: Article › 査読

抄録

In this paper, we provide a volume presentation of a hyperbolic fibered knot using the Bell polynomials. More precisely, we show that the hyperbolic volume of a fibered knot can be expressed in terms of the traces of powers of a monodromy matrix. We also show that the hyperbolic volume of the figure-eight knot is obtained by the asymptotics of a positive integer sequence consisting of the special values of the twisted Alexander invariants.

本文言語	English
ページ（範囲）	423-443
ページ数	21
ジャーナル	Tohoku Mathematical Journal
巻	76
号	3
DOI	https://doi.org/10.2748/tmj.20230208
出版ステータス	Published - 2024

ASJC Scopus subject areas

数学一般

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10.2748/tmj.20230208

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AB - In this paper, we provide a volume presentation of a hyperbolic fibered knot using the Bell polynomials. More precisely, we show that the hyperbolic volume of a fibered knot can be expressed in terms of the traces of powers of a monodromy matrix. We also show that the hyperbolic volume of the figure-eight knot is obtained by the asymptotics of a positive integer sequence consisting of the special values of the twisted Alexander invariants.

KW - Bell polynomial

KW - fibered knot

KW - figure-eight knot

KW - hyperbolic volume

KW - Twisted Alexander invariant

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UR - https://www.scopus.com/pages/publications/85205474701#tab=citedBy

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JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

IS - 3

ER -

A VOLUME PRESENTATION OF A FIBERED KNOT

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