Topology & Geometric Group Theory Seminar

Fall 2009

1:30 – 2:30, Malott 203

Tuesday, November 10

Matt Rathbun, UC Davis

High distance knots in any 3-manifold

Let M be a closed 3-manifold with a given Heegaard splitting. We show that after a single stabilization, some core of the stabilized splitting has arbitrarily high distance with respect to the splitting surface. This generalizes a result of Minsky, Moriah, and Schleimer for knots in S3. We also show that in the complex of curves, handlebody sets are either coarsely distinct or identical. We define the coarse mapping class group of a Heegaard splitting, and show that if (S, V, W) is a Heegaard splitting of genus ≥4, then CMCG(S,V,W) ≅ MCG(S, V,W). This is joint work with Marion Moore.

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