2006/04/05 by Ryan Derby-Talbot, Derby-Talbot, Ryan · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M99
paper · pdf · doi:10.48550/arxiv.math/0604115
21 pages, 18 figures. Version for publication. Generalization of the main theorem and minor changes in style and format
arxiv created 2007/04/29 · arxiv updated 2009/12/01
Let T be a separating incompressible torus in a 3-manifold M. Assuming that a genus g Heegaard splitting V ∪S W can be positioned nicely with respect to T (e.g. V ∪S W is strongly irreducible), we obtain an upper bound on the number of stabilizations required for V ∪S W to become isotopic to a Heegaard splitting which is an amalgamation along T. In particular, if T is a canonical torus in the JSJ decomposition of M, then the number of necessary stabilizations is at most 4g-4. As a corollary, this establishes an upper bound on the number of stabilizations required for V ∪S W and any Heegaard splitting obtained by a Dehn twist of V ∪S W along T to become isotopic.