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Geometry-Topology Seminar

Thursday, March 1, 2018 - 4:30pm

Michael Harrison

Lehigh University


University of Pennsylvania


A fibration of R^n by oriented copies of R^p is called skew if no two p-planes intersect nor contain parallel directions.  We discuss some interesting features of skew fibrations, and we exhibit a deformation retract from the space of fibrations of R^3 by skew oriented lines to its subspace of Hopf fibrations.  As a corollary of the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3.  We conclude with a discussion of skew fibrations in higher dimensions, including some surprising connections to the Hurwitz-Radon function and to vector fields on spheres.