16 citations · 52 across the 19 of their papers we have counts for
24 papers
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…
Geometry of the word problem for 3-manifold groups
Mark Brittenham, Susan Hermiller, Tim Susse
We provide an algorithm to solve the word problem in all fundamental groups of closed 3-manifolds; in particular, we show that these groups are autostackable. This provides a commo…
Homology and closure properties of autostackable groups
Mark Brittenham, Susan Hermiller, Ashley Johnson
Autostackability for finitely presented groups is a topological property of the Cayley graph combined with formal language theoretic restrictions, that implies solvability of the w…