15 citations · 30 across the 19 of their papers we have counts for
5 papers · 1 filter
Unknotting number and connected sums: The knots and
Mark Brittenham, Susan Hermiller
We show that the knots can be paired with a corresponding knot such that . As a consequence unknotting number fails to…
Unknotting number is not additive under connected sum
Mark Brittenham, Susan Hermiller
We give the first examples of a pair of knots , in the 3-sphere for which their unknotting numbers satisfy . This answers question 1.69(B) fro…
The smooth 4-genus of (the rest of) the prime knots through 12 crossings
Mark Brittenham, Susan Hermiller
We compute the smooth 4-genera of the prime knots with 12 crossings whose values, as reported on the KnotInfo website, were unknown. This completes the calculation of the smooth 4-…
A counterexample to the Bernhard-Jablan unknotting conjecture
Mark Brittenham, Susan Hermiller
We show that there is a knot satisfying the property that for each minimal crossing number diagram of the knot and each single crossing of the diagram, changing the crossing result…
4-moves and the Dabkowski-Sahi invariant for knots
Mark Brittenham, Susan Hermiller, Robert Todd
We study the 4-move invariant \crl\ for links in the 3-sphere developed by Dabkowski and Sahi, which is defined as a quotient of the fundamental group of the link complement. We de…