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### Proximity in the curve complex: boundary reduction and bicompressible surfaces

**Geometry/Topology**

Speaker: | Martin Scharlemann, UCSB |

Location: | 593 Kerr |

Start time: | Tue, Oct 26 2004, 2:10PM |

Abstract: Hartshorn proved that incompressible surfaces in a closed 3-manifold M provide a limit on distance for a Heegaard splitting of M. We show there is a relative version that extends to 3-manifolds with boundary. But the main and broader result is this: in the relative version, bicompressible but weakly incompressible surfaces can mostly be used instead of essential surfaces. Is the same true in the setting of Heegaard splittings? That is, does the genus of one Heegaard splitting put a bound on the distance of all others?

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