81 citations · 403 across the 47 of their papers we have counts for
6 papers · 2 filters
Computing closed essential surfaces in knot complements
Benjamin A. Burton, Alexander Coward, Stephan Tillmann
We present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences; h…
A new approach to crushing 3-manifold triangulations
Benjamin A. Burton
The crushing operation of Jaco and Rubinstein is a powerful technique in algorithmic 3-manifold topology: it enabled the first practical implementations of 3-sphere recognition and…
Computational topology and normal surfaces: Theoretical and experimental complexity bounds
Benjamin A. Burton, João Paixão, Jonathan Spreer
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to expone…
A fast branching algorithm for unknot recognition with experimental polynomial-time behaviour
Benjamin A. Burton, Melih Ozlen
It is a major unsolved problem as to whether unknot recognition - that is, testing whether a given closed loop in R^3 can be untangled to form a plain circle - has a polynomial tim…
Computational topology with Regina: Algorithms, heuristics and implementations
Benjamin A. Burton
Regina is a software package for studying 3-manifold triangulations and normal surfaces. It includes a graphical user interface and Python bindings, and also supports angle structu…
The complexity of detecting taut angle structures on triangulations
Benjamin A. Burton, Jonathan Spreer
There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manif…