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Seminar

Hamiltonian Seminar: Fibrations of R^3 and contact structures November 02, 2018 (02:00 PM PDT - 03:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Michael Harrison (Lehigh University)
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Abstract/Media

Is it possible to cover 3-dimensional space by a collection of lines, such that no two lines intersect and no two lines are parallel?  More precisely, does there exist a fibration of R^3 by pairwise skew lines?  We give some examples and provide a topological classification of these skew fibrations.  We continue with some recent results regarding contact structures on R^3 which are naturally induced by skew fibrations.  Finally, we discuss fibrations of R^3 which may contain parallel fibers, and discuss some structural results for such fibrations, as well as their relationship with contact structures.

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