3 papers
math.GT2024
Effective Computation of the Heegaard Genus of 3-Manifolds
Benjamin A. Burton, Finn Thompson
The Heegaard genus is a fundamental invariant of 3-manifolds. However, computing the Heegaard genus of a triangulated 3-manifold is NP-hard, and while algorithms exist, little work…
math.GT2024
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…
math.GT2020
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…