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On the Polynomial of the Dunwoody (1, 1)-knots
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  • Journal title : Kyungpook mathematical journal
  • Volume 52, Issue 2,  2012, pp.223-243
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2012.52.2.223
 Title & Authors
On the Polynomial of the Dunwoody (1, 1)-knots
Kim, Soo-Hwan; Kim, Yang-Kok;
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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 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.
Torus knot;(1, 1)-knot;(1, 1)-decomposition;Dunwoody 3-manifold;Alexander polynomial;Heegaard splitting;Heegaard diagram;
 Cited by
The Dual and Mirror Images of the Dunwoody 3-Manifolds, International Journal of Mathematics and Mathematical Sciences, 2013, 2013, 1  crossref(new windwow)
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