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http://dx.doi.org/10.5666/KMJ.2011.51.3.261

On Seifert Matrices of Symmetric Links  

Bae, Yong-Ju (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
Lee, In-Sook (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
Publication Information
Kyungpook Mathematical Journal / v.51, no.3, 2011 , pp. 261-281 More about this Journal
Abstract
In this paper, we will construct symmetric links by using the method adapted from the graph theory, and study a Seifert matrix of a symmetric link from the information of the Seifert matrix of the base link and the corresponding group action.
Keywords
symmetric link; periodic link; Seifert matrix; Alexander polynomial; determinant of a link; signature of a link;
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Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By SCOPUS : 0
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1 W. Lickorish, An Introduction to Knot Theory, Springer-Verlag New York, Inc., 1997.
2 Y. Miyazawa, Knots with a trivial coefficient polynomial, Kyungpook Math. J., 49(4)(2009), 801-809.   과학기술학회마을   DOI   ScienceOn
3 K. Murasugi, On the signature of links, Topology 9, (1970), 283-298.   DOI   ScienceOn
4 H. Seifert, U ber das geschlecht von knoten, Math. Ann, 110, 1934.
5 H. F. Trotter, On S-equivalence of Seifert matrices, Invent. Math., 20(1973), 173-207.   DOI
6 A. White, Graphs, Groups and Surfaces, Elsevier Science Publishers B.V, 1984.
7 Y. Choi, M. -J. Jeong and C. -Y. Park, Twist of knots and the Q -polynomials, Kyungpook Math. J., 44(2004), 449-467.   과학기술학회마을
8 S. Garoufalidis, Signatures of links and finite type invariants of cyclic branched covers, Tel Aviv Topology Conference: Rothenberg Festschrift, (1998), 87-97, Contemp. Math., 231, Amer. Math. Soc., Providence, RI, 1999.
9 J. L. Gross and T. W. Tucker, Topological graph theory, John Wiley & Sons, 1987.
10 L. H. Kauffman and L. R. Taylor, Signature of links, Trans. Amer. Math. Soc., 216(1976), 351-365.   DOI
11 A. Kawauchi, A survey of knot theory, Birkhauser -Verlag,Basel, Boston, and Berlin, 1996.
12 K. H. Ko and W. T. Song, Seifert matrices of periodic knots, J. Knot Theory Ramifications, 16(1)(2007), 45-57.   DOI   ScienceOn
13 J. Levine, The role of the Seifert matrix in knot theory, Actes du Congres International des Mathematiciens (Nice, 1970), Tome 2, pp. 95-98. Gauthier-Villars, Paris, 1971.
14 S. Y. Lee, M. -S. Park and M. Seo, The Seifert matrices of periodic links with rational quotients, Kyungpook Math. J., 47(2)(2007), 295-309.