Constructs Anosov flows in hyperbolic 3-manifolds, disproving a conjecture.
problem Proving existence of infinitely many distinct Anosov flows in certain 4-manifolds.
method Using Cannon-Thurston maps and pseudo-Anosov quasigeodesic flows.
result Infinitely many distinct Anosov flows in some 4-manifolds.
Study shows partial hyperbolicity leads to Anosov dynamics in 3-manifolds.
problem Understanding dynamics in hyperbolic 3-manifolds and Seifert manifolds.
method Classification of partially hyperbolic diffeomorphisms and pseudo-Anosov dynamics.
result Complete classification of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds and Seifert manifolds.
New method shows pseudo-Anosov flows on graph manifolds can be simplified.
problem Understanding pseudo-Anosov flows on graph manifolds.
method Constructing a partial Birkhoff section with genus one components that misses finitely many closed orbits.
result Every pseudo-Anosov flow on a graph manifold is almost equivalent to a totally periodic flow or a suspension Anosov flow.
Study on 3-manifolds admitting pseudo-Anosov maps on subsurfaces.
problem Which 3-manifolds admit pseudo-Anosov maps on incompressible subsurfaces?
method Determine self-homeomorphisms of 3-manifolds that restrict to pseudo-Anosov maps on subsurfaces.
result Self-homeomorphisms of irreducible 3-manifolds are isotopic to partially pseudo-Anosov homeomorphisms.
No contact Anosov diffeomorphisms exist on odd-dimensional manifolds.
problem Existence of contact Anosov diffeomorphisms on odd-dimensional manifolds.
method Analysis of Anosov diffeomorphisms and invariant contact structures.
result No invariant contact structure exists for Anosov diffeomorphisms on odd-dimensional manifolds.
Finitely many pseudo-Anosov flows without perfect fits in a 3-manifold.
problem Finite number of pseudo-Anosov flows without perfect fits in a 3-manifold.
method Analysis of veering triangulations and pseudo-Anosov flows.
result Finiteness of pseudo-Anosov flows without perfect fits.
Anosov flows in hyperbolic 3-manifolds are quasigeodesic if not R-covered.
problem Characterizing Anosov flows in hyperbolic 3-manifolds.
method Analyzing the properties of Anosov flows and foliations.
result Anosov flows in hyperbolic 3-manifolds are quasigeodesic if not R-covered.
Uniformizes compact complex manifolds via Anosov representations.
problem Uniformization of compact complex manifolds.
method Anosov homomorphisms with small limit sets.
result Local homeomorphism of character variety to Teichmüller space.
Classifies Anosov flows on figure-eight knot surgeries.
problem Classifying Anosov flows on Dehn surgeries on the figure-eight knot.
method Combining Plante's classification of M(0) with Schwider's branched surfaces.
result M(r) carries a unique Anosov flow if r is an integer, and no Anosov flow if r is not an integer.
Anosov geodesic flow proven in non-compact manifolds with negative curvature.
problem Proving Anosov geodesic flow in non-compact manifolds with negative curvature.
method Proving the geodesic flow is Anosov by showing average sectional curvature is negative and uniformly away from zero.
result Constructed a non-compact manifold with Anosov geodesic flow.
This paper classifies expanding attractors and non-transitive Anosov flows on specific knot and manifold spaces.
problem Classifying expanding attractors and non-transitive Anosov flows on specific knot and manifold spaces.
method Using the derived Anosov (DA) expanding attractor and the Franks-Williams manifold, the paper proves the uniqueness of these structures.
result The DA expanding attractor and the Franks-Williams non-transitive Anosov flow are the unique structures supported by N0 and M0 respectively. Deforms quasigeodesic flows to pseudo-Anosov ones.
problem Deforming quasigeodesic flows to pseudo-Anosov flows.
method Proves Calegari's conjecture by deforming flows.
result Proves every quasigeodesic flow can be deformed to pseudo-Anosov.
New 3D shapes found without certain flows.
problem Finding 3D shapes without specific flows.
method Using foliations and pseudo-Anosov flows, analyzing cusped hyperbolic 3-manifolds.
result First examples of 3D shapes without veering triangulations.
Anosov flows found on many hyperbolic 3-manifolds.
problem Existence of Anosov flows on hyperbolic 3-manifolds.
method Explicit construction of Anosov flows on fibered hyperbolic 3-manifolds.
result Positive density of fibered hyperbolic manifolds carrying Anosov flows.
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 that a pseudo-Anosov flow in a solv manifold is topologically equivalent to a susp…
Study on minimal foliations in 3D manifolds with specific conditions.
problem Characterizing minimal foliations in 3D manifolds.
method Analyzing Anosov foliations and their intersections.
result Necessary and sufficient conditions for orbit foliation of Anosov flows.
New maps connect universal circles to ideal sphere for hyperbolic manifolds.
problem Understanding universal circles for Anosov foliations with branching.
method Introduced a new type of Cannon--Thurston map for leftmost universal circles.
result Fundamental group acts on leftmost universal circle with pseudo-Anosov dynamics.
The study connects ECH capacities to Anosov flows, proving infinite capacities and obstructions.
problem Understanding ECH capacities and their relation to Anosov flows.
method Relating ECH capacities to Anosov flows dynamics, proving infinite capacities and obstructions.
result ECH capacities are infinite for many symplectic 4-manifolds, including cotangent disk bundles over surfaces of genus at least two.
Anosov representations of surface groups are complex manifolds.
problem Characterizing the geometry of Anosov representations of surface groups.
method Analyzing the character varieties of Anosov representations into $\SL(n , \C)$.
result Character varieties of Anosov representations are complex manifolds of specific dimension.
Embeds Riemannian manifolds with Anosov flows, linking classical and new theorems.
problem Embedding Riemannian manifolds with Anosov flows.
method Isometric embedding into a closed Riemannian manifold with Anosov geodesic flow.
result Direct link between classical and new theorems.
Generalizes Anosov flows to partially hyperbolic diffeomorphisms.
problem Classifying partially hyperbolic diffeomorphisms.
method Introducing collapsed Anosov flows and self orbit equivalences.
result All examples in Bonatti et al. belong to the collapsed Anosov flow class.
The study finds infinitely many periodic orbits that can be used to modify Anosov flows.
problem Can surgeries on periodic orbits of Anosov flows produce equivalent flows?
method Analyzing suspension Anosov flows, the study identifies pairs of periodic orbits that can be used to modify the flow.
result For some suspension Anosov flows, there exist infinitely many pairs of periodic orbits that can be used to modify the flow.
Proves existence of many non-R-covered Anosov flows on hyperbolic 3-manifolds.
problem Existence of many non-R-covered Anosov flows on hyperbolic 3-manifolds. method Description of clusters of lozenges in orbit spaces of constructed Anosov flows.
result Existence of hyperbolic 3-manifolds carrying many pairwise orbitally inequivalent quasi-geodesic Anosov flows.
Simplified approach to pseudo-Anosov flows on 3-manifolds.
problem Complexity in understanding pseudo-Anosov flows on 3-manifolds.
method Streamlined framework called Anosov-like group actions.
result Unified and simplified presentation of pseudo-Anosov flows.
Smoothly conjugate Anosov flows on 3D manifolds are actually smoothly conjugate.
problem Smoothly conjugate 3D Anosov flows are not always smoothly conjugate.
method Proved smooth rigidity for volume preserving Anosov flows on 3-manifolds.
result Smooth conjugacy implies smooth conjugacy for volume preserving Anosov flows.
We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show S3 does not admit conformally Anosov Reeb flows. We also give a Riemannian geometric condition on a metric compatible with a c…
We give complete classification of C^2-regular and non-degenerate projectively Anosov flows on three dimensional manifolds. More precisely, we prove that such a flow on a connected manifold must be either an Anosov flow or represented as a finite union of T2×[0,1]-models.
Reconstruct flows and manifolds from their boundary actions on circles.
problem Understanding and reconstructing flows and manifolds from their boundary actions.
method Reconstructing flows and manifolds from actions on circles with invariant almost laminations.
result Reconstructs flows and manifolds from their boundary actions, including pseudo-Anosov flows in 3-manifolds.
The paper proves rigidity results for Anosov flows and their orbit equivalences.
problem Characterizing orbit equivalences of Anosov flows and their dynamics.
method Using hyperbolic-like dynamics, the paper proves a spectral rigidity theorem and gives efficient criteria for orbit equivalences.
result Characterizes orbit equivalent flows in terms of fundamental group elements represented by periodic orbits.
Study non-transitive pseudo-Anosov flows using group actions.
problem Characterize pseudo-Anosov flows in 3-manifolds.
method Extend pseudo-Anosov action to non-transitive flows, use group actions on orbit spaces and boundary at infinity.
result Pseudo-Anosov flows in 3-manifolds are determined by their group actions on boundary at infinity.
We show that various classes of products of manifolds do not support transitive Anosov diffeomorphisms. Exploiting the Ruelle-Sullivan cohomology class, we prove that the product of a negatively curved manifold with a rational homology sphere does not support transitive Anosov diffeomorphisms. We extend this result to …
Constructs graph manifolds with many Anosov flows.
problem Finding graph manifolds supporting multiple Anosov flows.
method Cutting geodesic flows, pulling back to finite covers, and gluing compatible pairs of flows.
result Constructs graph manifolds with at least n Anosov flows for any n.
New insights into the geometry of flows on 3-manifolds.
problem Understanding the geometry of flows on 3-manifolds.
method Analyzing the action of pseudo-Anosov flows on Gromov-hyperbolic spaces.
result Genericity of non-periodic elements in the fundamental group.
New 3D shapes found without certain special flows.
problem Finding 3D shapes without specific special flows.
method Rational surgeries on the figure eight knot.
result First infinite family of hyperbolic 3-manifolds without tight projectively Anosov flows.
A long-standing conjecture asserts that any Anosov diffeomorphism of a closed manifold is finitely covered by a diffeomorphism which is topologically conjugate to a hyperbolic automorphism of a nilpotent manifold. In this paper, we show that any closed 4-manifold that carries a Thurston geometry and is not finitely cov…
We construct Anosov diffeomorphisms on manifolds that are homeomorphic to infranilmanifolds yet have exotic smooth structures. These manifolds are obtained from standard infranilmanifolds by connected summing with certain exotic spheres. Our construction produces Anosov diffeomorphisms of high codimension on infranilma…
Generalizes surgery techniques for projectively Anosov flows.
problem Creating new projectively Anosov flows from existing ones.
method Introducing a generalized Goodman surgery technique for projectively Anosov flows.
result Generates new examples of projectively Anosov flows on hyperbolic 3-manifolds.
In this paper, we show that a compact affine manifold endowed with an Affine Anosov transformation is finitely covered by a complete affine nilmanifold.
We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of T2×I-models. We also apply our method to rigidity problems of some group actions.
Odd covers have one Anosov flow, even covers have two.
problem Classifying Anosov flows on 3-manifolds with specific covers.
method Analyzing finite covers of geodesic flows on 3-manifolds.
result Odd covers result in one Anosov flow class, even covers in two.
This paper shows how pseudo-Anosov flows represent stable Hamiltonian classes and limits the ways 3-manifolds can be obtained from knots.
problem Understanding the canonical representatives of stable Hamiltonian classes and their implications for 3-manifolds.
method Explains the analogy between pseudo-Anosov flows and stable Hamiltonian classes and generalizes an argument to limit the ways 3-manifolds can be obtained from knots.
result There are finitely many pseudo-Anosov flows admitting positive Birkhoff sections on any given rational homology 3-sphere, and any 3-manifold can be obtained in at most finitely many ways as p/q surgery on a fibered hyperbolic knot in S3. Classifies pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
problem Classifying pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
method Generalized Anosov-like actions on bifoliated planes, ideal boundary analysis.
result Pseudo-Anosov flows on 3-manifolds are determined up to orbit equivalence by their ideal boundary actions.
New insights into pseudo-Anosov flows with special periodic orbits.
problem Understanding pseudo-Anosov flows with periodic orbits in 3-manifolds.
method Analyzing the topological features corresponding to trees of scalloped regions and classifying flows with the same free homotopy data.
result Explicit examples of flows with the same free homotopy data but not orbit equivalent.
In this paper we prove that if the geodesic flow of a {compact or non-compact} complete manifold without conjugate points is of the Anosov type, then the average of the integral of the sectional curvature along the geodesic is negative and away from zero from a uniform time. Moreover, in dimension two, if the manifold …
Study SRB measures for Anosov actions on manifolds.
problem Characterize SRB measures for Anosov actions.
method Use Ruelle-Taylor resonances and properties of Sinai-Ruelle-Bowen measures.
result SRB measures have properties like smooth disintegrations, positive basins, and are unique under certain conditions.
Study shows certain subgroups of fibered 3-manifolds are convex cocompact.
problem Understanding subgroups of fibered 3-manifolds in mapping class groups.
method Used the Birman exact sequence to show convex cocompactness.
result Finitely generated pseudo-Anosov subgroups are convex cocompact.
Proves transitivity of real Anosov diffeomorphisms with specific properties.
problem Transitivity of real Anosov diffeomorphisms with specific properties.
method Proves transitivity using specific properties of real Anosov diffeomorphisms.
result Proves transitivity of real Anosov diffeomorphisms.
Completes preliminary structures in 3D flows to foliations.
problem Characterizing completability of lamination pairs in 3-manifolds.
method General approach for various types of foliations and flows.
result Characterizes when lamination pairs can be completed to foliations.