Tsuyoshi KOBAYASHI Home Page

2009 Nara Topology Seminar

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u‰‰ŽÒFMarion Moore (Univ. of California, Davis)

u‰‰‘è–ځF High Distance Knots in closed 3-manifolds

Abstract: 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). This is joint work with Matt Rathbun.