60 citations · 228 across the 32 of their papers we have counts for
33 papers
Cohomology fractals, Cannon-Thurston maps, and the geodesic flow
David Bachman, Matthias Goerner, Saul Schleimer +1
Cohomology fractals are images naturally associated to cohomology classes in hyperbolic three-manifolds. We generate these images for cusped, incomplete, and closed hyperbolic thre…
Cohomology fractals
David Bachman, Saul Schleimer, Henry Segerman
We introduce cohomology fractals; these are certain images associated to a cohomology class on a hyperbolic three-manifold. They include images made entirely from circles, and also…
Computing Heegaard genus is NP-hard
David Bachman, Ryan Derby-Talbot, Eric Sedgwick
We show that {\sc Heegaard Genus }, the problem of deciding whether a triangulated 3-manifold admits a Heegaard splitting of genus less than or equal to , is NP-hard. Th…
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…
Normalizing Topologically Minimal Surfaces III: Bounded Combinatorics
David Bachman
We show that there are a finite number of possible pictures for a surface in a tetrahedron with local index . Combined with previous results, this establishes that any topologic…
Normalizing Topologically Minimal Surfaces II: Disks
David Bachman
We show that a topologically minimal disk in a tetrahedron with index is either a normal triangle, a normal quadrilateral, or a normal helicoid with boundary length 4(n+1). Thi…