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Bounding the
Kirby–Thompson invariant of spun knots
Román Aranda, Puttipong Pongtanapaisan, Scott A Taylor and Suixin (Cindy) Zhang |
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Algebraic & Geometric Topology 24 (2024) 3363–3399
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Abstract |
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A bridge trisection of a smooth surface in is a decomposition analogous to a bridge splitting of a link in . The Kirby–Thompson invariant of a bridge trisection measures its complexity in terms of distances between disk sets in the pants complex of the trisection surface. We give the first significant bounds for the Kirby–Thompson invariant of spun knots. In particular, we show that the Kirby–Thompson invariant of the spun trefoil is 15. |
Keywords
bridge trisections, pants complex
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Mathematical Subject Classification
Primary: 57K45
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References |
Publication
Received: 4 January 2022
Revised: 27 May 2022
Accepted: 8 November 2022
Published: 7 October 2024
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Authors |
| Román Aranda | |
| Department of Mathematical
Sciences Binghamton University Vestal, NY United States |
Department of Mathematics University of Nebraska – Lincoln Lincoln, NE United States |
| Puttipong Pongtanapaisan | |
| Department of Mathematical
Sciences University of Saskatchewan Saskatoon, SK Canada |
School of Mathematics and
Statistical Sciences Arizona State University Tempe, AZ United States |
| Scott A Taylor | |
| Department of Mathematics Colby College Waterville, ME United States |
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| Suixin (Cindy) Zhang | |
| Department of Mathematics University of California, Davis Davis, CA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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