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$C^{1,0}$ foliation
theory
William H Kazez and Rachel Roberts |
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Algebraic & Geometric Topology 19 (2019) 2763–2794
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Abstract |
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Transverse –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 –manifold . This is a combinatorial decomposition of 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 . 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 –dimensional techniques, and should generalize to prove corresponding results for codimension-one foliations in –dimensional manifolds. |
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Keywords
codimension-one foliation, flow, dimension-one foliation,
measured foliation, holonomy, flow box decomposition,
Denjoy blowup
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Mathematical Subject Classification 2010
Primary: 57M50
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References |
Publication
Received: 10 December 2016
Revised: 22 January 2019
Accepted: 5 February 2019
Published: 20 October 2019
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Authors |
| William H Kazez | |
| Department of Mathematics University of Georgia Athens, GA United States |
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| Rachel Roberts | |
| Department of Mathematics Washington University St Louis, MO United States |
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