81 citations · 403 across the 47 of their papers we have counts for
55 papers
Finding large counterexamples by selectively exploring the Pachner graph
Benjamin A. Burton, Alexander He
We often rely on censuses of triangulations to guide our intuition in -manifold topology. However, this can lead to misplaced faith in conjectures if the smallest counterexample…
Arc diagrams on 3-manifold spines
Jack Brand, Benjamin A. Burton, Zsuzsanna Dancso +3
We develop a theory of link projections to trivalent spines of 3-manifolds. We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projecti…
Hard Diagrams of the Unknot
Benjamin A. Burton, Hsien-Chih Chang, Maarten Löffler +5
We present three "hard" diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in…
On the hardness of finding normal surfaces
Benjamin A. Burton, Alexander He
For many fundamental problems in computational topology, such as unknot recognition and -sphere recognition, the existence of a polynomial-time solution remains unknown. A major…
Knot Diagrams of Treewidth Two
Hans L. Bodlaender, Benjamin Burton, Fedor V. Fomin +1
In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth…
Computing closed essential surfaces in 3-manifolds
Benjamin A. Burton, Stephan Tillmann
We present a practical algorithm to test whether a 3-manifold given by a triangulation or an ideal triangulation contains a closed essential surface. This property has important th…