2008/05/28 by Jesse Johnson, Johnson, Jesse · 3 citations
Computer Science · Mathematics · #Geometric and Algebraic Topology #Logic, programming, and type systems #math.GT #msc:57N10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0805.4422
22 pages, 7 figures
arxiv created 2008/05/28 · arxiv updated 2009/12/01
We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a combinatorial version of a proof by Hass, Thompson and Thurston of a similar theorem, but with an explicit bound in terms of distance. We also show that in a 3-manifold with boundary, the stable genus of a Heegaard splitting and a boundary stabilization of itself is bounded below by the same value.