2005/06/28 by Christopher Jerdonek, Jerdonek, Christopher
Computer Science · Mathematics · #57N10 (Primary) 57M50 (Secondary) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M50 #msc:57N10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0506558
Ph.D. dissertation, 73 pages, 22 figures (bitmapped EPS, as the arXiv cannot yet accept the vector-based PDF source)
arxiv created 2005/06/28 · openalex publication_date 2005/06/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct simple curves from immersed curves in the setting of handlebodies and Heegaard splittings. We define a measure of complexity we call girth for closed curves in a handlebody. We extend this complexity to Heegaard splittings and pose a conjecture about all Heegaard splittings. We prove a test case of this conjecture. Let S be a compact surface embedded in the boundary of a handlebody H. Then the minimum girth over all curves in S can be achieved by a simple closed curve. We also present algorithms to compute the girth of curves and surfaces.