Achiral 1-Cusped Hyperbolic 3-Manifolds Not Coming from Amphicheiral Null-homologous Knot Complements

K. Ichihara, I. D. Jong, Kouki Taniyama

    Research output: Contribution to journalArticle


    It is experimentally known that achiral hyperbolic 3-manifolds are quite sporadic at least among those with small volume, while we can find plenty of them as amphicheiral knot complements in the 3-sphere. In this paper, we show that there exist infinitely many achiral 1-cusped hyperbolic 3- manifolds not homeomorphic to any amphicheiral null-homologous knot complement in any closed achiral 3-manifold.

    Original languageEnglish
    Pages (from-to)1353-1361
    Number of pages9
    JournalLobachevskii Journal of Mathematics
    Issue number9
    Publication statusPublished - 2018 Nov 1



    • achiral hyperbolic 3-manifold
    • Amphicheiral knot
    • banding
    • chirally cosmetic filling
    • chirally cosmetic surgery

    ASJC Scopus subject areas

    • Mathematics(all)

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