7 citations · 28 across the 11 of their papers we have counts for
13 papers · 1 filter
Bounds in simple hexagonal lattice and classification of 11-stick knots
Yueheng Bao, Ari Benveniste, Marion Campisi +4
The stick number and the edge length of a knot type in the simple hexagonal lattice (sh-lattice) are the minimal numbers of sticks and edges required, respectively, to construct a…
Vertex distortion detects the unknot
Marion Campisi, Nicholas Cazet, David Crncevic +5
The first two authors introduced vertex distortion and showed that the vertex distortion of the unknot is trivial. It was conjectured that the vertex distortion of a knot is trivia…
Vertex distortion of lattice knots
Marion Campisi, Nicholas Cazet
The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the l1-norm. We show analogous…
Kirby-Thompson distance for trisections of knotted surfaces
Ryan Blair, Marion Campisi, Scott A. Taylor +1
We adapt work of Kirby-Thompson and Zupan to define an integer invariant of a bridge trisection of a smooth surface in …
The disk complex and topologically minimal surfaces in the 3-sphere
Marion Campisi, Luis Torres
We show that the disk complex of a genus Heegaard surface for the 3-sphere is homotopy equivalent to a wedge of -dimensional spheres. This implies that genus He…
Hyperbolic manifolds containing high topological index surfaces
Marion Campisi, Matt Rathbun
If a graph is in bridge position in a 3-manifold so that the graph complement is irreducible and boundary irreducible, we generalize a result of Bachman and Schleimer to prove that…
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…
Neighbors of knots in the Gordian graph
Ryan Blair, Marion Campisi, Jesse Johnson +2
We show that every knot is one crossing change away from a knot of arbitrarily high bridge number and arbitrarily high bridge distance.
Distance Two Links
Ryan Blair, Marion Campisi, Jesse Johnson +2
In this paper, we characterize all links in the 3-sphere with bridge number at least three that have a bridge sphere of distance two. We show that a link L has a bridge sphere of d…
Genus bounds bridge number for high distance knots
Ryan Blair, Marion Campisi, Jesse Johnson +2
If a knot K in a closed, orientable 3-manifold M has a bridge surface T with distance at least 3 in the curve complex of T - K, then the genus of any essential surface in its exter…
Exceptional and cosmetic surgeries on knots
Ryan Blair, Marion Campisi, Jesse Johnson +2
We show that the distance of a link with respect to a bridge surface of any genus determines a lower bound on the genus of essential surfaces and Heegaard surfaces in the manif…
alpha-sloped Generalized Heegaard splittings of 3-manifolds
Marion Moore Campisi
We generalize the definition of thin position of Scharlemann and Thompson for compact orientable 3-manifolds with torus boundary components and introduce -sloped generalized Hee…
High distance knots in closed 3-manifolds
Marion Moore Campisi, Matt Rathbun
Let M be a closed 3-manifold with a given Heegaard splitting. We show that after a single stabilization, some core of the stabilized splitting has arbitrarily high distance with re…