Geometry of alternating links on surfaces
Abstract
We consider links that are alternating on surfaces embedded in a compact 3-manifold. We show that under mild restrictions, the complement of the link decomposes into simpler pieces, generalising the polyhedral decomposition of alternating links of Menasco. We use this to prove various facts about the hyperbolic geometry of generalisations of alternating links, including weakly generalised alternating links described by the first author. We give diagrammatical properties that determine when such links are hyperbolic, find the geometry of their checkerboard surfaces, bound volume, and exclude exceptional Dehn fillings.
Keywords
Cite
@article{arxiv.1712.01373,
title = {Geometry of alternating links on surfaces},
author = {Joshua A. Howie and Jessica S. Purcell},
journal= {arXiv preprint arXiv:1712.01373},
year = {2019}
}
Comments
44 pages, 14 figures. V3: Updated exposition, and extended results on volume to manifolds with geodesic boundary. V2: Extended main results to links in any compact 3-manifold, not necessarily just those with torus boundary