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Abstract: Let be a codimension one foliation of an aspherical manifold M. Assume that has no vanishing cycles. If there is an aspherical dense leaf of , then each leaf of is aspherical. If is minimal and the universal covering of a leaf of is not k-connected, then the universal coverings of no leaves are k-connected. To cite this article: T. Yokoyama, C. R. Acad. Sci. Paris, Ser. I 347 (2009). [Copyright &y& Elsevier]

Abstract: Let M be an orientable connected closed surface and f be a homeomorphism on M. Suppose that the set is closed. Then the suspension of f satisfies one of the following conditions: 1) the closure of each element of it is toral; 2) there is a minimal set which is not locally connected. Moreover, we show that if the set of a homeomorphism f on a compact metrizable space is closed, then so is for any natural number k. [Copyright &y& Elsevier]

Abstract: Let be a transversely orientable codimension one minimal foliation without vanishing cycles of a manifold M and . We show that if the fundamental group of each leaf of has polynomial growth of degree k, then the foliation is without holonomy. [Copyright &y& Elsevier]