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2016 Independence of Roseman moves including triple points
Kengo Kawamura, Kanako Oshiro, Kokoro Tanaka
Algebr. Geom. Topol. 16(4): 2443-2458 (2016). DOI: 10.2140/agt.2016.16.2443


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.


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Kengo Kawamura. Kanako Oshiro. Kokoro Tanaka. "Independence of Roseman moves including triple points." Algebr. Geom. Topol. 16 (4) 2443 - 2458, 2016.


Received: 17 November 2015; Revised: 28 December 2015; Accepted: 9 January 2016; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1350.57028
MathSciNet: MR3546471
Digital Object Identifier: 10.2140/agt.2016.16.2443

Primary: 57Q45
Secondary: 57R45

Keywords: $S$–dependence , diagram , Roseman move , surface-link

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 4 • 2016
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