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THE ALEXANDER POLYNOMIAL OF (1,1)-KNOTS.
- Source :
-
Journal of Knot Theory & Its Ramifications . Nov2006, Vol. 15 Issue 9, p1119-1129. 11p. - Publication Year :
- 2006
-
Abstract
- In this paper we investigate the Alexander polynomial of (1,1)-knots, which are knots lying in a 3-manifold with genus one at most, admitting a particular decomposition. More precisely, we study the connections between the Alexander polynomial and a polynomial associated to a cyclic presentation of the fundamental group of an n-fold strongly-cyclic covering branched over the knot K, which we call the n-cyclic polynomial of K. In this way, we generalize to all (1,1)-knots, with the only exception of those lying in S2×S1, a result obtained by Minkus for 2-bridge knots and extended by the author and M. Mulazzani to the case of (1,1)-knots in S3. As corollaries some properties of the Alexander polynomial of knots in S3 are extended to the case of (1,1)-knots in lens spaces. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 15
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 23480218
- Full Text :
- https://doi.org/10.1142/S0218216506005019