Related papers: Reeb flows transverse to foliations

In this paper we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact and negatively curved basis. We also develop a notion of $F$-harmonic measure and prove that there exists a natural…

We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3-manifold with a stable Hamiltonian…

We investigate the combinatorial analogues, in the context of normal surfaces, of taut and transversely measured (codimension 1) foliations of 3-manifolds. We establish that the existence of certain combinatorial structures, a priori weaker…

We consider a fixed point free homeomorphsim $h$ of the closed band $B=\R\times[0,1]$ which leaves each leaf of a Reeb foliation on $B$ invariant. Assuming $h$ is the time one of various topological flows, we compare the restriction of the…

It is known that every contact form on a closed three-manifold has at least two simple Reeb orbits, and a generic contact form has infinitely many. We show that if there are exactly two simple Reeb orbits, then the contact form is…

Topology of Foliations of the Riemann Surfaces given by the real part of generic holomorphic 1-forms, is studied. Our approach is based on the notion of Transversal Canonical Basis of Cycles (TCB) instead of using just one closed…

The aim of this article is to apply a Floer theory to study symmetric periodic Reeb orbits. We define positive equivariant wrapped Floer homology using a (anti-)symplectic involution on a Liouville domain and investigate its algebraic…

We draw connections between the field of contact topology and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a…

We construct, for any given positive integer $n$, Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than $n$ boundary components. We use a connected sum operation for open books to…

This paper is devoted to the study of Gibbs u-states for the geodesic flow tangent to a foliation with negatively curved leaves. On the one hand we give sufficient conditions for the existence of transverse invariant measures. In particular…

We study the multiplicity problem for prime closed orbits of dynamically convex Reeb flows on the boundary of a star-shaped domain in $\mathbb{R}^{2n}$. The first of our two main results asserts that such a flow has at least $n$ prime…

Given a contact 3-manifold we consider the problem of when a given function can be realized as the Ricci curvature of a Reeb vector field for the contact structure. We will use topological tools to show that every admissible function can be…

We investigate the equivariant cohomology of the natural torus action on a K-contact manifold and its relation to the topology of the Reeb flow. Using the contact moment map, we show that the equivariant cohomology of this action is…

We show that any co-oriented closed contact manifold of dimension at least five admits a contact form such that the contact volume is arbitrarily small but the Reeb flow admits a global hypersurface of section with the property that the…

We prove the non--triviality of the Reeb flow for the (2n+1)--dimensional standard contact spheres inside the fundamental group of their contactomorphism group, n greater than 3. The argument uses the existence of homotopically non--trivial…

We use Lerman's contact cut construction to find a sufficient condition for Hamiltonian diffeomorphisms of compact surfaces to embed into a closed 3-manifold as Poincar\'e return maps on a global surface of section for a Reeb flow. In…

Thurston's triangulation conjecture asserts that every hyperbolic 3-manifold admits a geometric decomposition into ideal hyperbolic tetrahedra, a result proven only for certain special 3-manifolds. This paper presents combinatorial Ricci…

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…

The main theme of this paper is the dynamics of Reeb flows with symmetries on the standard contact sphere. We introduce the notion of strong dynamical convexity for contact forms invariant under a group action, supporting the standard…

Given a taut depth-one foliation $\mathcal{F}$ in a closed atoroidal 3-manifold $M$ transverse to a pseudo-Anosov flow $\phi$ without perfect fits, we show that the universal circle coming from leftmost sections $\mathfrak{S}_\mathrm{left}$…