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On the connectedness of the space of codimension one foliations on a closed 3-manifold

机译:关于余维空间在一个封闭的3流形上的连通性

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We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late 60's that every plane field can be deformed continuously to an integrable one, so the above inclusion induces a surjective map between connected components. We prove that this map is actually a bijection.
机译:我们研究了封闭三流形上光滑余维一叶的空间拓扑。我们将此空间视为所有光滑平面场的空间中包含的可积分平面场的空间。从60年代末开始就知道,每个平面场都可以连续变形为可积分场,因此上述包含会在连接的零部件之间产生一个射影图。我们证明该地图实际上是双射的。

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