Research ArticleNo Access

Computation of the knot symmetric quandle and its application to the plat index of surface-links

Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

E-mail Address: u444951d@ecs.osaka-u.ac.jp

https://doi.org/10.1142/S0218216524500056Cited by:0 (Source: Crossref)

Abstract

A surface-link is a closed surface embedded in the 4-space, possibly disconnected or non-orientable. Every surface-link can be presented by the plat closure of a braided surface, which we call a plat form presentation. The knot symmetric quandle of a surface-link $F$ is a pair of a quandle and a good involution determined from $F$ . In this paper, we compute the knot symmetric quandle for surface-links using a plat form presentation. As an application, we show that for any integers $g \geq 0$ and $m \geq 2$ , there exist infinitely many distinct surface-knots of genus $g$ whose plat indices are $m$ .

Keywords:

AMSC: 57K45, 57K10

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