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<p>Twisted right-angled Artin groups are defined through presentation based on mixed graphs. Each vertex corresponds to a generator, each undirected edge yields a commuting relation and each directed edge gives a Klein bottle relation. If there is no directed edge, then this reduces to an ordinary right-angled Artin group. There is a characterization of right-angled Artin groups which can be embedded in knot groups by Katayama. In this paper, we completely determine twisted right-angled Artin groups embedded in knot groups.</p>

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Twisted right-angled Artin groups embedded in knot groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月8日

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  • Keisuke Himeno,
  • Masakazu Teragaito

摘要

Twisted right-angled Artin groups are defined through presentation based on mixed graphs. Each vertex corresponds to a generator, each undirected edge yields a commuting relation and each directed edge gives a Klein bottle relation. If there is no directed edge, then this reduces to an ordinary right-angled Artin group. There is a characterization of right-angled Artin groups which can be embedded in knot groups by Katayama. In this paper, we completely determine twisted right-angled Artin groups embedded in knot groups.