대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권1호
  • /
  • Pages.203-223
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  • 2023
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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NEW FAMILIES OF HYPERBOLIC TWISTED TORUS KNOTS WITH GENERALIZED TORSION

  • Keisuke, Himeno (Graduate School of Advanced Science and Engineering Hiroshima University) ;
  • Masakazu, Teragaito (Department of Mathematics and Mathematics Education Hiroshima University)
  • 투고 : 2022.01.21
  • 심사 : 2022.04.07
  • 발행 : 2023.01.31
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초록

A generalized torsion element is an obstruction for a group to admit a bi-ordering. Only a few classes of hyperbolic knots are known to admit such an element in their knot groups. Among twisted torus knots, the known ones have their extra twists on two adjacent strands of torus knots. In this paper, we give several new families of hyperbolic twisted torus knots whose knot groups have generalized torsion. They have extra twists on arbitrarily large numbers of adjacent strands of torus knots.

키워드

과제정보

We would like to thank Kimihiko Motegi and Sangyop Lee for their helpful communications. We also thank the referee for careful reading.

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