10 citations · 24 across the 7 of their papers we have counts for
7 papers
Computing closed essential surfaces in knot complements
Benjamin A. Burton, Alexander Coward, Stephan Tillmann
We present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences; h…
Crossing changes and circular Heegaard splittings
Alexander Coward
We use technology from sutured manifold theory and the theory of Heegaard splittings to relate genus reducing crossing changes on knots in S^3 to twists on surfaces arising in circ…
Topological and physical knot theory are distinct
Alexander Coward, Joel Hass
Physical knots and links are one-dimensional submanifolds of R^3 with fixed length and thickness. We show that isotopy classes in this category can differ from those of classical k…
An upper bound on Reidemeister moves
Alexander Coward, Marc Lackenby
We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the same link. This leads to a conceptually simple solution to the e…
Ordering the Reidemeister moves of a classical knot
Alexander Coward
We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type.
Unknotting genus one knots
Alexander Coward, Marc Lackenby
For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is exactly one way to unknot it by means of a crossing change. In the c…