Abstract
Menasco proved that non-trivial links in the 3-sphere with connected prime alternating non-2-braid projections are hyperbolic. This was further extended to augmented alternating links wherein non-isotopic trivial components bounding disks punctured twice by the alternating link were added. Lackenby proved that the first and second collections of links together form a closed subset of the set of all finite volume hyperbolic 3-manifolds in the geometric topology. Here we prove that augmented cellular alternating links in I-bundles over closed surfaces are also hyperbolic and that in \(S \times I\), the cellular alternating links and the augmented cellular alternating links together form a closed subset of finite volume hyperbolic 3-manifolds in the geometric topology. Explicit examples of additional links in \(S \times I\) to which these results apply are included.
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We would like to give a special thanks to the referee for very helpful comments and corrections.
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Funding was provided by National Science Foundation (Grant No. DMS1659037).
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Adams, C., Capovilla-Searle, M., Li, D. et al. Augmented cellular alternating links in thickened surfaces are hyperbolic. European Journal of Mathematics 9, 100 (2023). https://doi.org/10.1007/s40879-023-00692-3
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DOI: https://doi.org/10.1007/s40879-023-00692-3