2012/10/29 by Tomoo Yokoyama, Yokoyama, Tomoo
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1210.7589
openalex publication_date 2012/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we define the recurrence and "non-wandering" for decompositions. The following inclusion relations hold for codimension one foliations on closed 3-manifolds: \minimal\ \sqcup \compact\ \subsetneq \pointwise almost periodic\ \subsetneq \recurrent\ \subsetneq \non-wandering\ \subsetneq \Reebless\. A non-wandering codimension one C2 foliation on a closed connected 3-manifold which has no leaf with uncountably many ends is minimal (resp. compact) if and only if it has no compact (resp. locally dense) leaves. In addition, the fundamental groups of all leaves of a codimension one transversely orientable C2 foliation F on a closed 3-manifold have the same polynomial growth if and only if F is without holonomy and has a leaf whose fundamental group has polynomial growth.