94 citations · 448 across the 56 of their papers we have counts for
4 papers · 1 filter
Knot concordances and alternating knots
Stefan Friedl, Charles Livingston, Raphael Zentner
There is an infinitely generated free subgroup of the smooth knot concordance group with the property that no nontrivial element in this subgroup can be represented by an alternati…
The four-genus of connected sums of torus knots
Charles Livingston, Cornelia A. Van Cott
We study the four-genus of linear combinations of torus knots: aT(p,q) # -bT(p',q'). Fixing positive p, q, p', and q', our focus is on the behavior of the four-genus as a function…
Signature Jumps and Alexander Polynomials for Links
Patrick M. Gilmer, Charles Livingston
We relate the jumps of the signature function of a link to the roots of its first nonzero higher Alexander polynomial.
Doubly slice knots with low crossing number
Charles Livingston, Jeffrey Meier
A knot in the three-sphere is doubly slice if it is the cross-section of an unknotted two-sphere in the four-sphere. For low-crossing knots, the most complete work to date gives a…