Link quandles are residually finite

Valeriy G. Bardakov, Mahender Singh, Manpreet Singh

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)679-690
Number of pages12
JournalMonatshefte fur Mathematik
Volume191
Issue number4
DOIs
Publication statusPublished - 1 Apr 2020

Keywords

  • Free product
  • Free quandle
  • Irreducible 3-manifold
  • Link quandle
  • Residually finite quandle
  • KNOT

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