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Graduate Student Geometry-Topology Seminar

Wednesday, April 16, 2008 - 11:00am

Elena Bogdan

Penn

Location

University of Pennsylvania

4C6 DRLB

In the 1920s Alexander proved that any knot in R^3 can be braided about the z-axis. In 1983, Bennequin proved the transverse case for R^3 with the standard contact structure. This says that a transverse knot can be taken into a braid form in such a way that the knot remains transverse to the contact planes throughout the process. I'll review Bennequin's proof and show how his result can be generalized to any closed, oriented, 3-dimensional manifold M, by looking at on open book decomposition for M together with a supported contact structure.