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Bing's Thm- The first step in a connection between knots and Heegaard Genus
Student-Run Geometry/Topology| Speaker: | Marion Moore, UC Davis |
| Location: | 2112 MSB |
| Start time: | Tue, Nov 13 2007, 1:10PM |
Description
It has been shown that given a closed 3-manifold M, M has a genus
g Heegaard splitting if and only if any knot in M can be ambient isotoped to
lie inside a genus g handlebody. The most straightforward case is S^3 (the
only manifold with a genus 0 Heegaard splitting), which gives us Bing's Thm:
If M is a closed orientable 3-manifold such that any knot in M lies interior
to a ball in M, then M is homeomorphic to S^3. In this talk I will give
background, and a proof to the theorem.