8 citations · 14 across the 11 of their papers we have counts for
9 papers · 1 filter
Genus two Goeritz equivalence in lens spaces
Brandy Doleshal, Matt Rathbun
In this paper, we consider the action of the Goeritz group for the genus two Heegaard splitting of the lens space with on the homology of the Heega…
Genus 2 Goeritz Equivalence in
Brandy Doleshal, Matt Rathbun
The Goeritz group of a genus Heegaard splitting of a 3-manifold is the group of isotopy classes of orientation-preserving automorphisms of the manifold that preserve the Heegaa…
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…
Complete classification of generalized crossing changes between GOF-knots
Kai Ishihara, Matt Rathbun
We analyze all monodromies of genus one fibered knots that possess clean or once-unclean arcs, and use this to determine all manifolds containing genus one fibered knots with gener…
Additional cases of positive twisted torus knots
Evan Amoranto, Brandy Doleshal, Matt Rathbun
A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in , the genus 2 Heegaard surface for . P…
Monodromy action on unknotting tunnels in fiber surfaces
Jessica E. Banks, Matt Rathbun
In "Tunnel one, fibered links", the second author showed that the tunnel of a tunnel number one, fibered link can be isotoped to lie as a properly embedded arc in the fiber surface…
Band surgeries and crossing changes between fibered links
Dorothy Buck, Kai Ishihara, Matt Rathbun +1
We characterize cutting arcs on fiber surfaces that produce new fiber surfaces, and the changes in monodromy resulting from such cuts. As a corollary, we characterize band surgerie…
Tunnel One, Fibered Links
Matt Rathbun
Let K be a tunnel number one, fibered link in S^3, with fiber F, and unknotting tunnel . We show that can be isotoped to lie in F.
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…