3 citations · 7 across the 5 of their papers we have counts for
8 papers
Normalizing Heegaard-Scharlemann-Thompson Splittings
David Bachman
We define a Heegaard-Scharlemann-Thompson (HST) splitting of a 3-manifold M to be a sequence of pairwise-disjoint, embedded surfaces, {F_i}, such that for each odd value of i, F_i…
Distance and bridge position
David Bachman, Saul Schleimer
J. Hempel's definition of the distance of a Heegaard surface generalizes to a complexity for a knot which is in bridge position with respect to a Heegaard surface. Our main result…
Non-parallel essential surfaces in knot complements
David Bachman
We show that if a knot or link has n thin levels when put in thin position then its exterior contains a collection of n disjoint, non-parallel, planar, meridional, essential surfac…
Surface bundles versus Heegaard splittings
David Bachman, Saul Schleimer
This paper studies Heegaard splittings of surface bundles via the curve complex of the fibre. The translation distance of the monodromy is the smallest distance it moves any vertex…
A note on Kneser-Haken finiteness
David Bachman
Kneser-Haken Finiteness asserts that for each compact 3-manifold M there is an integer c(M) such that any collection of k>c(M) closed, essential, 2-sided surfaces in M must contain…
Critical Heegaard Surfaces and Index 2 Minimal Surfaces
David Bachman
This paper contains the motivation for the study of critical surfaces. In previous work the only justification given for the definition of this new class of surfaces is the strengt…