LR number of spherical closed curves

Kuniyuki Takaoka*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    For a given oriented spherical closed curve with n transversal double points, we assign a cyclic word of length 2n on two letters L standing left and R standing right by reading the crossing sign so that each crossing point is read once L and once R. The LR number of the curve is the number of appearance of subwords LR in the cyclic word. We completely determine oriented spherical closed curves whose LR numbers are less than or equal to three.

    Original languageEnglish
    Pages (from-to)491-503
    Number of pages13
    JournalTokyo Journal of Mathematics
    Issue number2
    Publication statusPublished - 2015 Dec 1


    • LR number
    • LR word
    • Spherical closed curve

    ASJC Scopus subject areas

    • Mathematics(all)


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