Open Access
Translator Disclaimer
2009 The concordance genus of a knot, II
Charles Livingston
Algebr. Geom. Topol. 9(1): 167-185 (2009). DOI: 10.2140/agt.2009.9.167

Abstract

The concordance genus of a knot K is the minimum three-genus among all knots concordant to K. For prime knots of 10 or fewer crossings there have been three knots for which the concordance genus was unknown. Those three cases are now resolved. Two of the cases are settled using invariants of Levine’s algebraic concordance group. The last example depends on the use of twisted Alexander polynomials, viewed as Casson–Gordon invariants.

Citation

Download Citation

Charles Livingston. "The concordance genus of a knot, II." Algebr. Geom. Topol. 9 (1) 167 - 185, 2009. https://doi.org/10.2140/agt.2009.9.167

Information

Received: 17 October 2008; Accepted: 11 January 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1171.57004
MathSciNet: MR2482072
Digital Object Identifier: 10.2140/agt.2009.9.167

Subjects:
Primary: 57M25
Secondary: 57N70

Keywords: concordance, knot genus

Rights: Copyright © 2009 Mathematical Sciences Publishers

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.9 • No. 1 • 2009
MSP
Back to Top