The concordance genus of a knot, II

Livingston, Charles

doi:10.2140/agt.2009.9.167

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The concordance genus of a knot, II

Charles Livingston

Algebraic & Geometric Topology 9 (2009) 167–185

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.

Keywords

knot genus, concordance

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57N70

References

Publication

Received: 17 October 2008

Accepted: 11 January 2009

Published: 28 January 2009

Authors

Charles Livingston
Mathematics Department Indiana University Bloomington, IN 47405 USA

Volume 9, issue 1 (2009)