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Link quandles are residually finite

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Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work (Bardakov et al. in Proc Am Math Soc 147:3621–3633, 2019. https://doi.org/10.1090/proc/14488) residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these results and prove that free products of residually finite quandles are residually finite provided their associated groups are residually finite. As associated groups of link quandles are link groups, which are known to be residually finite, it follows that link quandles are residually finite.

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Acknowledgements

Bardakov acknowledges support from the Russian Science Foundation Project N 16-41-02006. Mahender Singh acknowledges support from INT/RUS/RSF/P-02 grant and SERB Matrics Grant MTR/2017/000018. Manpreet Singh thanks IISER Mohali for the PhD Research Fellowship.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk, Russia, 630090

    Valeriy G. Bardakov

  2. Novosibirsk State University, 2 Pirogova Street, Novosibirsk, Russia, 630090

    Valeriy G. Bardakov

  3. Novosibirsk State Agrarian University, Dobrolyubova Street, 160, Novosibirsk, Russia, 630039

    Valeriy G. Bardakov

  4. Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, P. O. Manauli, S. A. S. Nagar, Punjab, 140306, India

    Mahender Singh & Manpreet Singh

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  1. Valeriy G. Bardakov
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  2. Mahender Singh
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  3. Manpreet Singh
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Correspondence to Mahender Singh.

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Communicated by J. S. Wilson.

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Bardakov, V.G., Singh, M. & Singh, M. Link quandles are residually finite. Monatsh Math 191, 679–690 (2020). https://doi.org/10.1007/s00605-019-01336-z

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