16 citations · 96 across the 25 of their papers we have counts for
5 papers · 2 filters
Idempotents in Tangle Categories Split
Ryan Blair, Joshua Sack
In this paper we use 3-manifold techniques to illuminate the structure of the category of tangles. In particular, we show that every idempotent morphism in such a category natu…
The incompatibility of crossing number and bridge number for knot diagrams
Ryan Blair, Alexandra A. Kjuchukova, Makoto Ozawa
We define and compare several natural ways to compute the bridge number of a knot diagram. We study bridge numbers of crossing number minimizing diagrams, as well as the behavior o…
Height, trunk and representativity of knots
Ryan Blair, Makoto Ozawa
In this paper, we investigate three geometrical invariants of knots, the height, the trunk and the representativity. First, we give a conterexample for the conjecture which states…
Wirtinger systems of generators of knot groups
Ryan Blair, Alexandra Kjuchukova, Roman Velazquez +1
We define the {\it Wirtinger number} of a link, an invariant closely related to the meridional rank. The Wirtinger number is the minimum number of generators of the fundamental gro…
Distortion and the bridge distance of knots
Ryan Blair, Marion Campisi, Scott A. Taylor +1
We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in proportional to the minimum of the bridge distance and the brid…