Codimension one minimal foliations and the fundamental groups of leaves

Recurrent and Non-wandering properties for foliations

“…The C 2 condition and the growth condition are necessary, because the Denjoy foliation on T 2 is a non-R-closed foliation without holonomy and because there is a transversely orientable codimension one real-analytic minimal foliation with non-trivial holonomy such that each leaf has a fundamental group with exponential growth (e.g. Example 3.2 [21]). Note that the condition "the fundamental groups of all leaves have the same polynomial growth" in the previous theorem is necessary, because there is a codimension one minimal foliation on a closed 3-manifold with non-trivial holonomy each of whose leaves is either toral or planar.…”

“…Moreover, the polynomial growth condition is necessary, because there is a codimension one real-analytic minimal foliation on a closed 3-manifold with nontrivial holonomy such that all leaves are diffeomorphic to each other (e.g. Example 3.2 [21]). The author would like to know whether the pointwise almost periodicity can be replaced in the previous theorem with the non-wandering property.…”

“…In fact, there is a codimension one real-analytic minimal foliation on a closed 3-manifold with non-trivial holonomy such that all leaves are diffeomorphic to each other (e.g. Example 3.2 [21]). The polynomial growth of the fundamental group of a manifold implies the following statement.…”

Codimension one minimal foliations whose leaves have fundamental groups with the same polynomial growth

“…In [YT08], we have considered the following question: how is the minimal foliation without null homotopic closed transversals if the fundamental group of each leaf is isomorphic to an elementary group?…”

“…Example 3.2. [YT08]). In this paper, we consider the above question for the minimal foliations without vanishing cycles and obtain the following result.…”