Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 423-443 |
| Number of pages | 21 |
| Journal | Tohoku Mathematical Journal |
| Volume | 76 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2024 |
Keywords
- Bell polynomial
- fibered knot
- figure-eight knot
- hyperbolic volume
- Twisted Alexander invariant
ASJC Scopus subject areas
- General Mathematics
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