4 papers · 1 filter
An algorithm to construct one-vertex triangulations of Heegaard splittings
Alexander He, James Morgan, Em K. Thompson
Following work of Jaco and Rubinstein (2006), which (non-constructively) proved that any 3-manifold admits a one-vertex layered triangulation, we present an algorithm, with impleme…
Connecting 3-manifold triangulations with unimodal sequences of elementary moves
Benjamin A. Burton, Alexander He
A key result in computational 3-manifold topology is that any two triangulations of the same 3-manifold are connected by a finite sequence of bistellar flips, also known as Pachner…
A Practical Algorithm for Knot Factorisation
Alexander He, Eric Sedgwick, Jonathan Spreer
We present an algorithm for computing the prime factorisation of a knot, which is practical in the following sense: using Regina, we give an implementation that works well for inpu…
Crushing Surfaces of Positive Genus
Benjamin A. Burton, Thiago de Paiva, Alexander He +1
The operation of crushing a normal surface has proven to be a powerful tool in computational -manifold topology, with applications both to triangulation complexity and to algori…