Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Polynomial of the Dunwoody (1, 1)-knots

  • Received : 2010.05.08
  • Accepted : 2012.02.19
  • Published : 2012.06.23
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Abstract

There is a special connection between the Alexander polynomial of (1, 1)-knot and the certain polynomial associated to the Dunwoody 3-manifold ([3], [10] and [13]). We study the polynomial(called the Dunwoody polynomial) for the (1, 1)-knot obtained by the certain cyclically presented group of the Dunwoody 3-manifold. We prove that the Dunwoody polynomial of (1, 1)-knot in $\mathbb{S}^3$ is to be the Alexander polynomial under the certain condition. Then we find an invariant for the certain class of torus knots and all 2-bridge knots by means of the Dunwoody polynomial.

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References

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Cited by

  1. The Dual and Mirror Images of the Dunwoody 3-Manifolds vol.2013, 2013, https://doi.org/10.1155/2013/103209