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Independence of Roseman
moves including triple points
Kengo Kawamura, Kanako Oshiro and Kokoro Tanaka |
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Algebraic & Geometric Topology 16 (2016) 2443–2458
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Abstract |
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The Roseman moves are seven types of local modifications for surface-link diagrams in –space which generate ambient isotopies of surface-links in –space. In this paper, we focus on Roseman moves involving triple points, one of which is the famous tetrahedral move, and discuss their independence. For each diagram of any surface-link, we construct a new diagram of the same surface-link such that any sequence of Roseman moves between them must contain moves involving triple points (and the number of triple points of the two diagrams are the same). Moreover, we find a pair of diagrams of an –knot such that any sequence of Roseman moves between them must involve at least one tetrahedral move. |
Keywords
surface-link, diagram, Roseman move, $S$–dependence
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Mathematical Subject Classification 2010
Primary: 57Q45
Secondary: 57R45
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References |
Publication
Received: 17 November 2015
Revised: 28 December 2015
Accepted: 9 January 2016
Published: 12 September 2016
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Authors |
| Kengo Kawamura | |
| Department of Mathematics Osaka City University 3-3-138 Sugimoto-cho Sumiyoshi-ku Osaka 558-8585 Japan |
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| Kanako Oshiro | |
| Department of Information and
Communication Sciences Sophia University 7-1 Kioi-cho Chiyoda-ku Tokyo 102-8554 Japan |
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| Kokoro Tanaka | |
| Department of Mathematics Tokyo Gakugei University 4-1-1 Nukuikita-machi Koganei-shi Tokyo 184-8501 Japan |
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