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<p>幾何学関係の皆様<br>
トポロジー関係の皆様<br>
<br>
以下の講演会を行いますのでお知らせします。<br>
<br>
坪井俊<br>
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2018年06月22日(金)
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16:00-17:00 数理科学研究科棟(駒場) 128号室
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[講演者] Michael Harrison 氏 (Lehigh University)
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[講演題目] Fibrations of R<sup class="moz-txt-sup"><span
style="display:inline-block;width:0;height:0;overflow:hidden">^</span>3</sup>
by oriented lines <br>
[講演概要]<br>
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.<br>
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<p>＝＝＝＝＝＝＝<br>
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