Volume 9, issue 1 (2009)

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The concordance genus of a knot, II

Charles Livingston

Algebraic & Geometric Topology 9 (2009) 167–185
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
Primary: 57M25
Secondary: 57N70