8 citations · 10 across the 3 of their papers we have counts for
4 papers
Degeneration of Heegaard genus, a survey
David Bachman, Ryan Derby-Talbot
We survey known (and unknown) results about the behavior of Heegaard genus of 3-manifolds constructed via various gluings. The constructions we consider are (1) gluing together two…
Stabilizations of Heegaard splittings of graph manifolds
Ryan Derby-Talbot
We show that after one stabilization, a strongly irreducible Heegaard splitting of suitably large genus of a graph manifold is isotopic to an amalgamation along a modified version…
Stabilizing Heegaard splittings of toroidal 3-manifolds
Ryan Derby-Talbot
Let be a separating incompressible torus in a 3-manifold . Assuming that a genus Heegaard splitting can be positioned nicely with respect to (e.g. $V \c…
Non-isotopic Heegaard splittings of Seifert fibered spaces
David Bachman, Ryan Derby-Talbot
We find a geometric invariant of isotopy classes of strongly irreducible Heegaard splittings of toroidal 3-manifolds. Combining this invariant with a theorem of R Weidmann, proved…