81 citations · 403 across the 47 of their papers we have counts for
5 papers · 2 filters
Enumerating fundamental normal surfaces: Algorithms, experiments and invariants
Benjamin A. Burton
Computational knot theory and 3-manifold topology have seen significant breakthroughs in recent years, despite the fact that many key algorithms have complexity bounds that are exp…
Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations
Benjamin A. Burton
It is important to have effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a…
Triangulating a Cappell-Shaneson knot complement
Ryan Budney, Benjamin A. Burton, Jonathan Hillman
We show that one of the Cappell-Shaneson knot complements admits an extraordinarily small triangulation, containing only two 4-dimensional simplices.
Computing the crosscap number of a knot using integer programming and normal surfaces
Benjamin A. Burton, Melih Ozlen
The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap…
Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations
Benjamin A. Burton
Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms i…