81 citations · 403 across the 47 of their papers we have counts for
4 papers · 2 filters
The complexity of the normal surface solution space
Benjamin A. Burton
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important a…
The Weber-Seifert dodecahedral space is non-Haken
Benjamin A. Burton, J. Hyam Rubinstein, Stephan Tillmann
In this paper we settle Thurston's old question of whether the Weber-Seifert dodecahedral space is non-Haken, a problem that has been a benchmark for progress in computational 3-ma…
Quadrilateral-octagon coordinates for almost normal surfaces
Benjamin A. Burton
Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional…
Converting between quadrilateral and standard solution sets in normal surface theory
Benjamin A. Burton
The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a hig…