## 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 S^{3}. 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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