94 citations · 448 across the 56 of their papers we have counts for
67 papers
Rank-expanding satellite operators on the topological knot concordance group
Charles Livingston
Given a fixed knot P in a solid torus and any knot K in S^3, one can form the satellite of K with pattern P. This operation induces a self-map of the concordance group of knots in…
An Upsilon torsion function for knot Floer homology
Samantha Allen, Charles Livingston
Heegaard Floer theory produces chain complexes associated to knots. Viewed as modules over polynomial rings, such complexes yield torsion invariants that offer constraints on cobor…
Signed clasp numbers and four-genus bounds
Charles Livingston
There exist knots having positive and negative four-dimensional clasp numbers zero but having four-genus, and hence clasp number, arbitrarily large. Such examples were first constr…
Branched covers and rational homology balls
Charles Livingston
The concordance group of knots in the three-sphere contains an infinite subgroup generated by elements of order two, each one of which is represented by a knot K with the property…
Intrinsic symmetry groups of links
Charles Livingston
The set of isotopy classes of ordered n-component links in the 3-sphere is acted on by the symmetric group via permutation of the components. The intrinsic symmetry group of the li…
Cobordism distance on the projective space of the knot concordance group
Charles Livingston
The cobordism distance on the knot concordance group is used to define a measure of how close two knots are to being linearly dependent. Roughly stated, d(K,J) is defined by minimi…