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On The Disjoint Curve Property
Student-Run Geometry/Topology Seminar| Speaker: | Carlos Barrera-Rodriguez, UC Davis |
| Location: | 2112 MSB |
| Start time: | Thu, Jan 18 2007, 1:10PM |
Given a Heegaard Splitting (H_1,H_2,F) of a 3-manifold we say that it has the Disjoint Curve Property (DCP) if there are essential curves a,b,c on F such that a bounds a disk in H_1, b bounds a disk in H_2 and c is disjoint from a and b. It turns out that a manifold with a genus 2 Heegaard Splitting which have the DCP can be well understood in a very nice way. In this talk (based on a paper by Abigail Thompson) we will be introducing some basic notions of Heegaard Splittings and proving interesting results obtained using the DCP.