Hyperbolic knotoids

Author(s)
Adams, Colin; Bonat, Alexandra; Chande, Maya; Chen, Joye; Jiang, Maxwell; ... Show more
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Abstract
In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints. A variety of knot invariants have been extended to knotoids. Here we provide definitions of hyperbolicity for both spherical and planar knotoids. We prove that the product of hyperbolic spherical knotoids is hyperbolic and the volumes add. We also determine the least volume of a rational spherical knotoid and provide various classes of hyperbolic knotoids. We also include tables of hyperbolic volumes for both spherical and planar knotoids.
Date issued
2024-07-15
URI
https://hdl.handle.net/1721.1/159828
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
European Journal of Mathematics
Publisher
Springer International Publishing
Citation
Adams, C., Bonat, A., Chande, M. et al. Hyperbolic knotoids. European Journal of Mathematics 10, 43 (2024).
Version: Author's final manuscript
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