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Shadows of $2$–knots
and complexity
Hironobu Naoe |
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Algebraic & Geometric Topology 24 (2024) 4651–4695
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Abstract |
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We introduce a new invariant for a –knot in , called the shadow-complexity, based on the theory of Turaev shadows, and we give a characterization of –knots with shadow-complexity at most . Specifically, we show that the unknot is the only –knot with shadow-complexity and that there exist infinitely many –knots with shadow-complexity . |
Keywords
2–knot, Turaev shadow, 4–manifold, complexity, banded
unlink diagram
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Mathematical Subject Classification
Primary: 57K40, 57K45
Secondary: 57R65
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References |
Publication
Received: 9 November 2022
Revised: 9 May 2023
Accepted: 2 August 2023
Published: 17 December 2024
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Authors |
| Hironobu Naoe | |
| Department of Mathematics Tokyo Institute of Technology Tokyo Japan |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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