2010/04/26 by Jesse Johnson, Johnson, Jesse
Mathematics · #57M #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M
paper · pdf · doi:10.48550/arxiv.1004.4669
83 pages, 17 figures. The definition of the complex of surfaces has been modified in Version 2 to fix an ambiguity in the original definition
openalex publication_date 2010/04/26 · arxiv created 2011/07/10 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that given a partially flat angled ideal triangulation for a 3-manifold M with boundary (as defined by Lackenby), there is an algorithm to produce a list of Heegaard splittings for M such that below a given genus g, each isotopy class appears exactly once. In particular, this algorithm determines precisely when two almost normal surfaces represent Heegaard splittings that are isotopic in the ambient 3-manifold. A closely related algorithm determines the smallest genus common stabilization of any two Heegaard splittings on the list. The methods, in fact, characterize isotopies between Heegaard surfaces in any triangulation, but the existence of infinitely many normal surfaces of the same genus prevents this characterization from being algorithmic in general.