Tohoku Mathematical Journal
2024
September
SECOND SERIES VOL. 76, NO. 3

Tohoku Math. J.
76 (2024), 423-443

Title A VOLUME PRESENTATION OF A FIBERED KNOT

Author Hiroshi Goda and Takayuki Morifuji

(Received November 30, 2022, revised February 8, 2023)
Abstract. n 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.

Mathematics Subject Classification. Primary 57K14; Secondary 57K10, 57K32, 05A19.
Key words and phrases. Twisted Alexander invariant, hyperbolic volume, fibered knot, Bell polynomial, figure-eight knot.

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