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Geometry-Topology Seminar

Tuesday, January 30, 2018 - 4:30pm

Herman Gluck



University of Pennsylvania

DRL 4N30

This is the beginning of an experiment, a Geometry-Topology "Show and Tell" Seminar, in which faculty describe their current interests. The talks will be on Tuesdays at 4:30 PM in DRL 4N30. Future speakers are Wolfgang Ziller (2/6), Davi Maximo (2/13), Sasha Kirillov (2/20), Robin Pemantle (2/27), David Futer (3/20) and Randy Kamien (3/27).

Given a smooth fibration of the unit 3-sphere by great circles, we show that the distribution of 2-planes orthogonal to the fibres is a contact structure, a fact well known in the special case of the Hopf fibrations. 

The proof expresses hypothesis and conclusion as differential inequalities involving functions on disks transverse to the fibres, and shows that one inequality implies the other.