81 citations · 403 across the 47 of their papers we have counts for
42 papers · 1 filter
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…
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…
The HOMFLY-PT polynomial is fixed-parameter tractable
Benjamin A. Burton
Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 t…
Finding non-orientable surfaces in 3-manifolds
Benjamin A. Burton, Arnaud de Mesmay, Uli Wagner
We investigate the complexity of finding an embedded non-orientable surface of Euler genus in a triangulated -manifold. This problem occurs both as a natural question in low…