Bipyramid Decompositions of Multi-crossing Link Complements
Colin Adams, Gregory Kehne
TL;DR
This paper introduces bipyramid decompositions for multi-crossing link complements, providing new volume bounds for hyperbolic links based on their projections, and demonstrates these bounds with specific tiling examples.
Contribution
It generalizes bipyramid decompositions to multi-crossing links and establishes new volume bounds for hyperbolic links from their projections.
Findings
New upper bounds on hyperbolic link volumes
Decomposition into bipyramids for multi-crossing projections
Realization of bounds through infinite tiling weaves
Abstract
Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link L into bipyramids, given any multi-crossing projection of L. When L is hyperbolic, this gives new upper bounds on the volume of L given its multi-crossing projection. These bounds are realized by three closely related infinite tiling weaves.
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