%0 Journal Article
%T High distance knots in closed 3-manifolds
%A Marion Moore Campisi
%A Matt Rathbun
%J Mathematics
%D 2009
%I arXiv
%X 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 Heeegaard splitting, and show that if (S, V, W) is a Heegaard splitting of genus greater than or equal to 2, then the coarse mapping class group of (S,V,W) is isomorphic to the mapping class group of (S, V,W).
%U http://arxiv.org/abs/0911.3675v2