Ryan Derby-Talbot

activity

20052016

most citedDegeneration of Heegaard genus, a survey

8 citations · 19 across the 9 of their papers we have counts for

collaborators

10 papers

math.GT2016

Computing Heegaard genus is NP-hard

David Bachman, Ryan Derby-Talbot, Eric Sedgwick

We show that {\sc Heegaard Genus $\leq g$ }, the problem of deciding whether a triangulated 3-manifold admits a Heegaard splitting of genus less than or equal to $g$ , is NP-hard. Th…

math.GT2015

Locally Helical Surfaces have bounded twisting

David Bachman, Ryan Derby-Talbot, Eric Sedgwick

A topologically minimal surface may be isotoped into a normal form with respect to a fixed triangulation. If the intersection with each tetrahedron is simply connected, then the pi…

math.GT2012

Almost normal surfaces with boundary

David Bachman, Ryan Derby-Talbot, Eric Sedgwick

We show that a strongly irreducible and boundary-strongly irreducible surface can be isotoped to be almost normal in a triangulated 3-manifold.

math.GT2010

Surfaces that become isotopic after Dehn filling

David Bachman, Ryan Derby-Talbot, Eric Sedgwick

We show that after generic filling along a torus boundary component of a 3-manifold, no two closed, 2-sided, essential surfaces become isotopic, and no closed, 2-sided, essential s…

math.GT2009★ 1 cited

Heegaard structure respects complicated JSJ decompositions

David Bachman, Ryan Derby-Talbot, Eric Sedgwick

Let $M$ be a 3-manifold with torus boundary components $T_{1}$ and $T_{2}$ . Let $ϕ : T_{1} \to T_{2}$ be a homeomorphism, $M_{ϕ}$ the manifold obtained from $M$ by gluing $T_{1}$ to $T_{2}$ …

math.GT2009★ 1 cited

Stabilization, amalgamation, and curves of intersection of Heegaard splittings

Ryan Derby-Talbot

We address a special case of the Stabilization Problem for Heegaard splittings, establishing an upper bound on the number of stabilizations required to make a Heegaard splitting of…