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Symmetries and hidden
symmetries of $(\epsilon, d_L)$–twisted knot complements
Neil R Hoffman, Christian Millichap and William Worden |
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Algebraic & Geometric Topology 22 (2022) 601–656
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Abstract |
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We analyze symmetries, hidden symmetries and commensurability classes of –twisted knot complements, which are the complements of knots that have a sufficiently large number of twists in each of their twist regions. These knot complements can be constructed via long Dehn fillings on fully augmented link complements. We show that such knot complements have no hidden symmetries, which implies that there are at most two other knot complements in their respective commensurability classes. Under mild additional hypotheses, we show that these knots have at most four (orientation-preserving) symmetries and are the only knot complements in their respective commensurability classes. Finally, we provide an infinite family of explicit examples of –twisted knot complements that are the unique knot complements in their respective commensurability classes obtained by filling a fully augmented link complement with four crossing circles. |
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Keywords
commensurability classes of knot complements, hidden
symmetries, orbifolds, Dehn filling, fully augmented links
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Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27, 57M50
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References |
Publication
Received: 23 September 2019
Revised: 29 November 2020
Accepted: 30 December 2020
Published: 3 August 2022
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Authors |
| Neil R Hoffman | |
| Department of Mathematics Oklahoma State University Stillwater, OK United States |
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| https://math.okstate.edu/people/nhoffman/ | |
| Christian Millichap | |
| Department of Mathematics Furman University Greenville, SC United States |
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| https://www.furman.edu/people/christian-millichap/ | |
| William Worden | |
| Department of Mathematics Rice University Houston, TX United States |
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| https://www.wtworden.org/ | |
