Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Invariant Trace Fields of Chain Links

  • Ryou, Kazuhiro (Department of Mathematics, Tokyo Institute of Technology)
  • Received : 2014.11.03
  • Accepted : 2015.12.10
  • Published : 2016.03.23
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Abstract

In this paper, we compute the trace field of C(2, s), the complement of two component chain link with s left half twists in ${\mathbb{S}}^3$, for every s. As a result, for every $n{\in}{\mathbb{N}}{\backslash}\{1\}$, we can find $s{\in}{\mathbb{Z}}$ such that the degree of the trace field of C(2, s) is n. We also prove that if for fixed p, the degree of the trace field of C(p, s) runs over ${\mathbb{N}}{\backslash}\{1\}$, then p is contained in {1, 2, 4, 8}.

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References

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