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Geometry-Topology Seminar

Friday, October 26, 2012 - 2:30pm

Emmy Murphy

MIT

Location

Bryn Mawr College

Park Science Building, Room 336

The goal of this talk will be to define loose Legendrian knots in high dimensions, and state their classification. No prior knowledge of contact topology will be assumed; we will start by defining and drawing pictures of Legendrian knots in high dimensions. We will then define what it means for a Legendrian to be loose, and prove some of their basic existence properties, such as their C^0 density and their existence in any formal isotopy class. We will then state their classification up to Legendrian isotopy, and discuss various applications of their classification to high dimensional symplectic/contact topology. Time permitting, we will contrast with the 3-dimensional setting, and present some relevant open questions.