2023/04/12 by Peter Feller, Alessandro Sisto, Feller, Peter +3
Mathematics · #57K32 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57K32
paper · pdf · doi:10.48550/arxiv.2304.05990
10 pages. 1 figure. V2: Improvements based on referee comments. Multiple constants improved; one factor-of-two error fixed. Comments welcome!
arxiv created 2026/07/31 · arxiv updated 2026/08/03
We consider the family of Heegaard splittings of genus g at least two which are defined via a gluing map that is the n-th power of the Dehn twist along a curve that satisfies a natural topological assumption, namely pared acylindricity. We show that if n is at least 14, then the Heegaard splitting has a hyperbolic metric for which the simple closed curve defining the Dehn twist is a closed geodesic of length at least 1.24/(n2g) and at most 37.5/n2