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Topological canal foliations. (English) Zbl 1417.57024

This article introduces the notion of a topological canal foliation of a 3-dimensional manifold. Furthermore it classifies the compact oriented 3-manifolds that support such foliations. This notion generalizes that of a geometric canal foliation previously studied by R. Langevin and P. G. Walczak [J. Math. Soc. Japan 64, No. 2, 659–682 (2012; Zbl 1297.53021)]. The latter are codimension-1 foliations of 3-manifolds of constant curvature whose leaves, when lifted to the universal covering space form, are surfaces which are the envelopes of one-parameter families of spheres. Topological canal foliations are defined by topological rather than by geometric conditions.

MSC:

57R30 Foliations in differential topology; geometric theory
53C12 Foliations (differential geometric aspects)

Citations:

Zbl 1297.53021
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