Independence of Roseman moves including triple points

Kawamura, Kengo¹ ; Oshiro, Kanako² ; Tanaka, Kokoro³

¹Department of Mathematics, Osaka City University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka 558-8585, Japan
²Department of Information and Communication Sciences, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
³Department of Mathematics, Tokyo Gakugei University, 4-1-1 Nukuikita-machi, Koganei-shi, Tokyo 184-8501, Japan

Algebraic and Geometric Topology, Tome 16 (2016) no. 4, pp. 2443-2458

Résumé

The Roseman moves are seven types of local modifications for surface-link diagrams in 3–space which generate ambient isotopies of surface-links in 4–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 S2–knot such that any sequence of Roseman moves between them must involve at least one tetrahedral move.

Détail

DOI : 10.2140/agt.2016.16.2443

Classification : 57Q45, 57R45
Keywords: surface-link, diagram, Roseman move, $S$–dependence

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