Invariant Trace Fields of Chain Links

• Journal title : Kyungpook mathematical journal
• Volume 56, Issue 1,  2016, pp.257-271
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2016.56.1.257
Title & Authors
Invariant Trace Fields of Chain Links
Ryou, Kazuhiro;

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 $\small{{\mathbb{S}}^3}$, for every s. As a result, for every $\small{n{\in}{\mathbb{N}}{\backslash}\{1\}}$, we can find $\small{s{\in}{\mathbb{Z}}}$ 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 $\small{{\mathbb{N}}{\backslash}\{1\}}$, then p is contained in {1, 2, 4, 8}.
Keywords
Language
English
Cited by
References
1.
J. Hoste and P. Shanahan, Trace fields of twist knot, J. Knot Theory and its Ramifications, 10(2001), 625-639.

2.
C. Maclachlan and A. Reid, The Arithmetic of Hyperbolic 3-Manifolds, Springer, New York, 2003.

3.
K. Matsuzaki and M. Taniguchi, Hyperbolic Manifolds and Kleinian Groups, Oxford University Press, Oxford, 1998.

4.
W. Neumann and A. Reid, Arithmetic of hyperbolic manifolds, In Topology'90, 273-310, de Gruyter, Berlin, 1990.