Seminar
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| Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
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Secondary Mathematics Subject Classification
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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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