Volumes of Montesinos links
Kathleen Finlinson, Jessica S. Purcell
TL;DR
This paper establishes bounds on the volume of Montesinos links based on their diagram's combinatorial properties, completing the understanding for all cases.
Contribution
It extends previous volume bounds to all Montesinos links, including those with three or four tangles, filling a significant gap in the literature.
Findings
Bounded volumes for all Montesinos links using diagram combinatorics
Unified previous results for different tangle counts
Provided explicit upper and lower volume bounds
Abstract
We show that the volume of any Montesinos link can be bounded above and below in terms of the combinatorics of its diagram. This was known for Montesinos links with at most two tangles, and those with at least five tangles. We complete the result for the remaining cases.
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