81 citations · 403 across the 47 of their papers we have counts for
9 papers · 2 filters
On the Complexity of Immersed Normal Surfaces
Benjamin A. Burton, Éric Colin de Verdière, Arnaud de Mesmay
Normal surface theory, a tool to represent surfaces in a triangulated 3-manifold combinatorially, is ubiquitous in computational 3-manifold theory. In this paper, we investigate a…
An edge-based framework for enumerating 3-manifold triangulations
Benjamin A. Burton, William Pettersson
A typical census of 3-manifolds contains all manifolds (under various constraints) that can be triangulated with at most n tetrahedra. Al- though censuses are useful resources for…
2-manifold recognition is in logspace
Benjamin A. Burton, Murray Elder, Arkadius Kalka +1
We prove that the homeomorphism problem for 2-manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected -connectivity problem in…
The cusped hyperbolic census is complete
Benjamin A. Burton
From its creation in 1989 through subsequent extensions, the widely-used "SnapPea census" now aims to represent all cusped finite-volume hyperbolic 3-manifolds that can be obtained…
Combinatorial Seifert fibred spaces with transitive cyclic automorphism group
Benjamin Burton, Jonathan Spreer
In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a…
Courcelle's theorem for triangulations
Benjamin A. Burton, Rodney G. Downey
In graph theory, Courcelle's theorem essentially states that, if an algorithmic problem can be formulated in monadic second-order logic, then it can be solved in linear time for gr…