Geodesic
C1,0 foliation theory
Kazez, William1 ; Roberts, Rachel2
1 Department of Mathematics, University of Georgia, Athens, GA, United States
2 Department of Mathematics, Washington University, St Louis, MO, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 6, pp. 2763-2794

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.2763
Classification : 57M50
Keywords: codimension-one foliation, flow, dimension-one foliation, measured foliation, holonomy, flow box decomposition, Denjoy blowup

Kazez, William 1 ; Roberts, Rachel 2

1 Department of Mathematics, University of Georgia, Athens, GA, United States
2 Department of Mathematics, Washington University, St Louis, MO, United States 
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Kazez, William; Roberts, Rachel. C1,0 foliation theory. Algebraic and Geometric Topology, Tome 19 (2019) no. 6, pp. 2763-2794. doi: 10.2140/agt.2019.19.2763

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