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Twisted
braids
Shudan Xue and Qingying Deng |
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Vol. 17 (2024), No. 4, 543–568
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Abstract |
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Twisted knot theory, introduced by M. O. Bourgoin, is a generalization of virtual knot theory. It naturally yields the notion of a twisted braid, which is closely related to the notion of a virtual braid due to Kauffman. We first prove that any twisted link can be described as the closure of a twisted braid, which is unique up to certain basic moves. This is the analogue of the Alexander theorem and the Markov theorem for classical braids and links. Then we also give reduced presentations for the twisted braid group and the flat twisted braid group. These reduced presentations are based on the fact that these twisted braid groups on strands are generated by a single braiding element and a single bar element plus the generators of the symmetric group on letters. |
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Keywords
twisted link, twisted braids, braiding link diagram,
reduced presentation
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Mathematical Subject Classification
Primary: 57K10
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Supplementary material |
Milestones
Received: 26 July 2021
Revised: 12 May 2022
Accepted: 31 May 2023
Published: 2 October 2024
Communicated by Józef H. Przytycki
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Authors |
| Shudan Xue | |
| School of Mathematics and
Computational Science Xiangtan University Xiangtan China |
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| Qingying Deng | |
| School of Mathematics and
Computational Science Xiangtan University Xiangtan China |
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| © 2024 MSP (Mathematical Sciences Publishers). |
