Simplicial volume of links from link diagrams
Oliver Dasbach, Anastasiia Tsvietkova
TL;DR
This paper extends the understanding of how the simplicial volume of link complements behaves under diagram modifications, providing a refined volume bound based on twist lengths by analyzing toroidal decompositions.
Contribution
It generalizes the invariance of hyperbolic volume to simplicial volume and introduces a refined upper bound for link volume using toroidal decompositions and twist analysis.
Findings
Simplicial volume remains unchanged under certain diagram modifications.
A new upper bound for link volume based on twist lengths.
Analysis of toroidal decompositions enhances volume estimates.
Abstract
The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a link diagram, and a suitable 3-punctured sphere is present in the complement. We generalize this to the simplicial volume of link complements by analyzing the corresponding toroidal decompositions. We then use it to prove a refined upper bound for the volume in terms of twists of various lengths for links.
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