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The Thurston Norm
Student-Run Geometry/Topology| Speaker: | Yvonne Lai, UC Davis |
| Location: | 593 Kerr |
| Start time: | Thu, Dec 9 2004, 1:10PM |
Description
In 1985, Bill Thurston showed: suppose M is a compact
atoroidal orientable 3-maniofld such that the rank of H_2(M,\partial M; \mathbb{Z}) is greater than 1. Then M contains an embedded superincompressible surface which is not a fiber in a fibration of M over S^1 and which represents a nontrivial element of H_2.
His proof relies on the Thurston norm, which we will introduce. Time permitting, we'll sketch the proof. More likely, we'll just have time to introduce the norm and cover some background material.