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2019 $C^{1,0}$ foliation theory
William H Kazez, Rachel Roberts
Algebr. Geom. Topol. 19(6): 2763-2794 (2019). DOI: 10.2140/agt.2019.19.2763

Abstract

Transverse 1–dimensional foliations play an important role in the study of codimension-one foliations. In Geom. Topol. Monogr. 19 (2015) 21–72, the authors introduced the notion of flow box decomposition of a 3–manifold M. This is a combinatorial decomposition of M that reflects both the structure of a given codimension-one foliation and that of a given transverse dimension-one foliation, and that is amenable to inductive strategies.

In this paper, flow box decompositions are used to extend some classical foliation results to foliations that are not C2. Enhancements of well-known results of Calegari on smoothing leaves, Dippolito on Denjoy blowup of leaves, and Tischler on approximations by fibrations are obtained. The methods developed are not intrinsically 3–dimensional techniques, and should generalize to prove corresponding results for codimension-one foliations in n–dimensional manifolds.

Citation

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William H Kazez. Rachel Roberts. "$C^{1,0}$ foliation theory." Algebr. Geom. Topol. 19 (6) 2763 - 2794, 2019. https://doi.org/10.2140/agt.2019.19.2763

Information

Received: 10 December 2016; Revised: 22 January 2019; Accepted: 5 February 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07142618
MathSciNet: MR4023328
Digital Object Identifier: 10.2140/agt.2019.19.2763

Subjects:
Primary: 57M50

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 6 • 2019
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