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KNOTS IN HOMOLOGY LENS SPACES DETERMINED BY THEIR COMPLEMENTS

  • Ichihara, Kazuhiro (Department of Mathematics College of Humanities and Sciences Nihon University) ;
  • Saito, Toshio (Department of Mathematics Joetsu University of Education)
  • Received : 2021.07.08
  • Accepted : 2021.11.05
  • Published : 2022.07.31
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Abstract

In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let M be a homology lens space with H1(M; ℤ) ≅ ℤp and K a not null-homologous knot in M. We show that, K is determined by its complement if M is non-hyperbolic, K is hyperbolic, and p is a prime greater than 7, or, if M is actually a lens space L(p, q) and K represents a generator of H1(L(p, q)).

Keywords

Acknowledgement

The authors would like to thank Tetsuya Ito for useful discussions, and also thank to the anonymous referee for reading the paper carefully and providing thoughtful comments.

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