Papers › An algorithm to construct one-vertex triangulations of Heegaard splittings
An algorithm to construct one-vertex triangulations of Heegaard splittings
Alexander He, James Morgan, Em K. Thompson
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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 implementation using Regina, that uses a combinatorial presentation of a Heegaard diagram to construct a generalised notion of a layered triangulation. We show that work of Husz\'ar and Spreer (2019) extends to our construction: given a genus-g Heegaard splitting, our algorithm generates a triangulation with cutwidth bounded above by 4g-2. Beyond Heegaard splittings, our construction actually extends to a natural generalisation of Dehn fillings: given a one-vertex triangulation with a genus-g boundary component B, we can construct a one-vertex triangulation of any 3-manifold obtained by filling B with a handlebody. To demonstrate the usefulness of our algorithm, we present findings from preliminary computer searches using this algorithm.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections