162 citations · 690 across the 42 of their papers we have counts for
44 papers
The underlying manifold of a low-volume hyperbolic 3-orbifold
David Futer, Peter B. Shalen
This paper proves strong restrictions on the underlying topological space of a closed, orientable hyperbolic 3-orbifold \orbM whose volume satisfies a certain upper bound. For inst…
Hyperbolic manifolds without positive spun triangulations
David Futer, Jessica S. Purcell, Saul Schleimer
Using a result of Choi, we provide the first examples of pairs consisting of a closed hyperbolic three-manifold and a simple closed geodesic, such that there is no positive spun id…
Arithmeticity and commensurability of links in thickened surfaces
David Futer, Rose Kaplan-Kelly
The family of right-angled tiling links consists of links built from regular 4-valent tilings of constant-curvature surfaces that contain one or two types of tiles. The complements…
Excluding cosmetic surgeries on hyperbolic 3-manifolds
David Futer, Jessica S. Purcell, Saul Schleimer
This paper employs knot invariants and results from hyperbolic geometry to develop a practical procedure for checking the cosmetic surgery conjecture on any given one-cusped manifo…
Homotopy equivalent boundaries of cube complexes
Talia Fernós, David Futer, Mark Hagen
A finite-dimensional CAT(0) cube complex is equipped with several well-studied boundaries. These include the Tits boundary (which depends on the CAT(0) metric), the Roller boun…
Large volume fibred knots of fixed genus
Kenneth L. Baker, David Futer, Jessica S. Purcell +1
We show that, for hyperbolic fibred knots in the three-sphere, the volume and the genus are unrelated. Furthermore, for such knots, the volume is unrelated to strong quasipositivit…