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Bridge trisections
and classical knotted surface theory
Jason Joseph, Jeffrey Meier, Maggie Miller and Alexander Zupan |
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Vol. 319 (2022), No. 2, 343–369
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Abstract |
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We seek to connect ideas in the theory of bridge trisections with other well-studied facets of classical knotted surface theory. First, we show how the normal Euler number can be computed from a tri-plane diagram, and we use this to give a trisection-theoretic proof of the Whitney–Massey theorem, which bounds the possible values of this number in terms of the Euler characteristic. Second, we describe in detail how to compute the fundamental group and related invariants from a tri-plane diagram, and we use this, together with an analysis of bridge trisections of ribbon surfaces, to produce an infinite family of knotted spheres that admit nonisotopic bridge trisections of minimal complexity. |
Keywords
knotted surface, bridge trisection, 2-knot, trisection
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Mathematical Subject Classification
Primary: 57K45
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Milestones
Received: 30 December 2021
Revised: 20 May 2022
Accepted: 27 May 2022
Published: 11 September 2022
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Authors |
| Jason Joseph | |
| Department of Mathematics Rice University Houston, TX United States |
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| Jeffrey Meier | |
| Department of Mathematics Western Washington University Bellingham, WA United States |
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| Maggie Miller | |
| Department of Mathematics Stanford University Stanford, CA United States |
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| Alexander Zupan | |
| Department of Mathematics University of Nebraska–Lincoln Lincoln, NE United States |
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