[geometry-ml:03372] Michael Harrison氏講演会20180622

[Tsuboi, Takashi]

幾何学関係の皆様
トポロジー関係の皆様

以下の講演会を行いますのでお知らせします。

坪井俊
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2018年06月22日(金)
16:00-17:00   数理科学研究科棟(駒場) 128号室
[講演者]　Michael Harrison 氏 (Lehigh University)
[講演題目] Fibrations of R^3 by oriented lines
[講演概要]
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 complete topological classification 
of such objects, by exhibiting a deformation retract from the space of 
skew fibrations of R^3 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 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 when such objects induce contact structures.

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