Related papers: Surgery on Anosov flows using bi-contact geometry

We introduce a generalization of Goodman surgery to the category of projectively Anosov flows. This construction is performed along a knot that is simultaneously Legendrian and transverse for a supporting bi-contact structure. If the flow…

We discuss a metric description of the divergence of a (projectively) Anosov flow in dimension 3, in terms of its associated growth rates and give metric and contact geometric characterizations of when a projectively Anosov flow is Anosov.…

To any Anosov flow X on a 3-manifold Fe1 associated a bi-foliated plane (a plane endowed with two transverse foliations Fs and Fu) which reflects the normal structure of the flow endowed with the center-stable and center unstable…

We provide an exposition of a `horizontal' generalization of Goodman's surgery operation on (pseudo-)Anosov flows. This operation is performed by cutting along a specific kind of annulus that is transverse to the flow and regluing with a…

The purpose of this paper is to classify Anosov flows on the 3-manifolds obtained by Dehn surgeries on the figure-eight knot. This set of 3-manifolds is denoted by M(r) (r is a ratioanl number), which contains the first class of hyperbolic…

We make a first step towards connecting the theory of veering triangulations and bicontact structures as tools for studying (pseudo-)Anosov flows: We show that given a veering triangulation corresponding to an Anosov flow with orientable…

We show that a transitive Anosov flow with orientable stable and unstable foliations that either (i) admits a Birkhoff section whose first return map is a Penner type pseudo-Anosov map, or (ii) is totally periodic admits a genus one…

In this paper, we show that any topologically transitive Anosov flow on a closed three-dimensional manifold with the orientable weak stable and unstable foliations turns into an R-covered one by a Goodman-Fried surgery along periodic…

We produce infinitely many examples of Anosov flows in closed 3-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of…

We present a new approach to hyperbolic plugs, via a construction of bicontact plugs on 3-manifolds with boundary that are surface bundles over the circle. The boundary components are quasi transverse tori, and we prove a gluing theorem…

We show that the action on its orbit space induced by a pseudo-Anosov flow on a closed $3$-manifold (and more general Anosov-like actions) can be seen as an isometric action on a Gromov-hyperbolic space. When the flow is not $\R$-covered,…

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 apply the matching functions technique in the setting of contact Anosov flows which satisfy a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman-Ornstein~\cite{FO}. Namely, we show that if two…

We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and discuss a framework to use tools from contact and symplectic geometry and topology in the study of Anosov dynamics. We also discuss some…

We prove a rigidity result for group actions on the line whose elements have what we call "hyperbolic-like" dynamics. Using this, we give a spectral rigidity theorem for $\mathbb{R}$-covered Anosov flows on 3-manifolds, characterizing orbit…

In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a…

Let $(M, g)$ be a complete Riemannian manifold without focal points and curvature bounded below. We prove that when the average of the sectional curvature in tangent planes along geodesics is negative and uniformly away from zero, then the…

We construct a class of Riemannian metrics in closed surfaces of genus greater than one, having Anosov geodesic flows, and some regions of positive curvature, such that for each such surface, there exists a smooth curve of conformal…

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…

We prove that in dimension 3, Anosov flows which are $\mathbb{R}$-covered and skewed are orbit equivalent to Reeb-Anosov flows. We characterize the existence of an invariant contact form or of a Birkhoff section with a given boundary, in…