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7 papers · 1 filter
Roots of Dehn twists
Darryl McCullough, Kashyap Rajeevsarathy
D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotop…
Arc distance equals level number
Sangbum Cho, Darryl McCullough, Arim Seo
A knot K in 1-bridge position with respect to a genus-g Heegaard surface in a 3-manifold can be moved by isotopy through knots in 1-bridge position until it lies in a union of n pa…
Tunnel leveling, depth, and bridge numbers
Sangbum Cho, Darryl McCullough
This is the third of three papers that refine and extend portions of our earlier preprint, "The depth of a knot tunnel." Together, they rework the entire preprint. In this paper, w…
Constructing knot tunnels using giant steps
Sangbum Cho, Darryl McCullough
This is the first of three papers that refine and extend portions of our earlier preprint, "Depth of a knot tunnel." Together, they rework the entire preprint. H. Goda, M. Scharlem…
Homeomorphisms of the 3-sphere that preserve a Heegaard splitting of genus two
Sangbum Cho
Let be the group of isotopy classes of orientation preserving homeomorphisms of that preserve a Heegaard splitting of genus two. In this paper, we use a tree i…
Orientation-reversing free actions on handlebodies
Antonio F. Costa, Darryl McCullough
We examine free orientation-reversing group actions on orientable handlebodies, and free actions on nonorientable handlebodies. A classification theorem is obtained, giving the equ…