Sharp bounds on some classical knot invariants

Kearton, C.; Wilson, S.M.J.

Abstract

There are obvious inequalities relating the Nakanishi index of a knot, the bridge number, the degree 2n of the Alexander polynomial and the length of the chain of Alexander ideals. We give examples for every positive value of n to show that these bounds are sharp.

Citation

Kearton, C., & Wilson, S. (2003). Sharp bounds on some classical knot invariants. Journal of Knot Theory and Its Ramifications, 12(06), 805-817. https://doi.org/10.1142/s0218216503002792

• Journal Article Type: Article
• Publication Date: Sep 1, 2003
• Deposit Date: Feb 15, 2008
• Journal: Journal of Knot Theory and Its Ramifications
• Print ISSN: 0218-2165
• Electronic ISSN: 1793-6527
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 06
• Pages: 805-817
• DOI: https://doi.org/10.1142/s0218216503002792
• Keywords: Nakanishi index, Knot module, Bridge number, Alexander polynomial, Alexander ideal, Nonmaximal order, Arithmetic order, Hermitian order, Hermitian form, Fitting ideal.
• Public URL: https://durham-repository.worktribe.com/output/1598772
• Publisher URL: http://www.worldscinet.com/jktr/12/preserved-docs/1206/S0218216503002792.pdf