TL;DR
This paper demonstrates that in hyperbolic fibered knots within closed 3-manifolds, volume and genus are independent, and it addresses a related question about volumes of certain mapping tori.
Contribution
It establishes the independence of volume and genus for hyperbolic fibered knots and answers a specific question about mapping tori volumes.
Findings
Volume and genus are unrelated for hyperbolic fibered knots.
Provides an answer to a question about volumes of mapping tori as double branched covers.
Abstract
We prove that for hyperbolic fibered knots in any closed, connected, oriented 3-manifold the volume and genus are unrelated. As an application we answer a question of Hirose, Kalfagianni, and Kin about volumes of mapping tori that are double branched covers.
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