94 citations · 448 across the 56 of their papers we have counts for
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math.GT2008★ 7 cited
The concordance genus of a knot, II
Charles Livingston
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 con…
math.GT2008
The algebraic concordance order of a knot
Charles Livingston
Levine defined the rational algebraic knot concordance group and proved that each nontrivial element is of order two, of order four, or of infinite order. The determination of the…
math.GT2008★ 2 cited
Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation
Chris Herald, Paul Kirk, Charles Livingston
Given a knot complement X and its p-fold cyclic cover X_p, we identify twisted polynomials associated to 1-dimensional linear representations of the fundamental group of X_p with t…