相关论文: Rigidity of pseudo-Anosov flows transverse to R-co…
We study the transverse geometric behavior of 2-dimensional foliations in 3-manifolds. We show that an R-covered transversely orientable foliation with Gromov hyperbolic leaves in a closed 3-manifold admits a regulating, transverse…
Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost transverse to a quasigeodesic pseudo-Anosov flow. We show that the leaves of the foliation in the universal cover extend…
We study minimal transverse foliations which are $R$-covered. If in addition the dimension of the ambient manifold is $3$, and the foliations are Anosov foliations we give necessary and sufficient conditions for the intersected foliation to…
We study R-covered foliations of 3-manifolds from the point of view of their transverse geometry. For an R-covered foliation in an atoroidal 3-manifold M, we show that M-tilde can be partially compactified by a canonical cylinder S^1_univ x…
In this paper, we study transversely holomorphic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove that for Anosov flows on smooth compact manifolds, the strong unstable (respectively, stable)…
We establish a rigidity result for the unstable foliations of transitive Anosov flows on 3-manifolds: if the unstable foliations of two such flows are equivalent (that is, if there exists a homeomorphism mapping one foliation to the other),…
The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it…
Given a general pseudo-Anosov flow in a three manifold, the orbit space of the lifted flow to the universal cover is homeomorphic to an open disk. We compactify this orbit space with an ideal circle boundary. If there are no perfect fits…
We show that for a taut foliation F with one-sided branching of an atoroidal 3-manifold M, one can construct a pair of genuine laminations with solid torus complementary regions which bind every leaf of F in a geodesic lamination. These…
We produce examples of taut foliations of hyperbolic 3-manifolds which are R-covered but not uniform --- ie the leaf space of the universal cover is R, but pairs of leaves are not contained in bounded neighborhoods of each other. This…
Motivated by problems in the study of Anosov and pseudo-Anosov flows on 3-manifolds, we characterize when a pair $(L^+, L^-)$ of subsets of transverse laminations of the circle can be completed to a pair of transverse foliations of the…
In this article we study the topological structure of the lifts to the universal of the stable and unstable foliations of $3$-dimensional Anosov flows. In particular we consider the case when these foliations do not have Hausdorff leaf…
We show that if $\mathcal{F}_1$ and $\mathcal{F}_2$ are two transverse minimal foliations on $M = T^1S$ then either they intersect in an Anosov foliation or there exists a Reeb-surface in the intersection foliation. The existence of a Reeb…
We consider two transitive $3$-dimensional Anosov flows which do not preserve volume and which are continuously conjugate to each other. Then, disregarding certain exceptional cases, such as flows with $C^1$ regular stable or unstable…
We define and study the foliated centralizer: the group of $C^\infty$ centralizer elements of the lift of an Anosov system on a non-compact manifold which additionally preserve the stable and unstable foliations. When the Anosov system is…
We first prove rigidity results for pseudo-Anosov flows in prototypes of toroidal 3-manifolds: we show that a pseudo-Anosov flow in a Seifert fibered manifold is up to finite covers topologically equivalent to a geodesic flow and we show…
In this article, we study the knots realized by periodic orbits of R-covered Anosov flows in compact 3-manifolds. We show that if two orbits are freely homotopic then in fact they are isotopic. We show that lifts of periodic orbits to the…
We present a combinatorial approach to the existence of foliations and contact structures transverse to a given pseudo-Anosov flow. Let $\varphi$ be a transitive pseudo-Anosov flow on a closed oriented 3-manifold. Our main technical result…
We provide sufficient conditions for smooth conjugacy between two Anosov endomorphisms on the 2-torus. From that, we also explore how the regularity of the stable and unstable foliations implies smooth conjugacy inside a class of…
We introduce the notion of a pseudo-Anosov contact structure, which admits a type of singular contact form with pseudo-Anosov Reeb flow. We prove that contact homology detects the free homotopy classes of closed orbits of any pseudo-Anosov…