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.
