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.
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.
Study angle structures on pseudo 3-manifolds, proving existence for some cases.
problem Determining if hyperbolic 3-manifolds can have angle structures.
method Examined triangulated pseudo 3-manifolds with area-curvature angle structures, establishing sufficient and necessary conditions.
result Compact hyperbolic 3-manifolds with totally geodesic boundary can have angle structures.
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.
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.
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.
The paper studies pseudo-isotopies of spherical 3-manifolds and computes ranks of certain groups.
problem Computing ranks of abelian groups related to spherical 3-manifolds.
method Surgery on theta-graphs embedded in spherical 3-manifolds, study of pseudo-isotopy behavior under suspension.
result Lower bounds of ranks of abelian groups π0Diff(X,∂) are computed. 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.
Method calculates Z2-Thurston norm for Seifert 3-manifolds using pseudo-horizontal surfaces.
problem Computing Z2-Thurston norm for Z2-homology classes in orientable Seifert 3-manifolds. method Using pseudo-horizontal surfaces, we provide a necessary and sufficient criterion for their existence, calculate non-orientable genera, and develop an algorithm to compute the Z2-Thurston norm. result We successfully compute the Z2-Thurston norm for every Z2-homology class in orientable Seifert 3-manifolds. 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.
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 Veech groups in fibered 3-manifolds, proving no parabolics for fibers.
problem Characterizing Veech groups in fibered 3-manifolds.
method Analyzing pseudo-Anosov monodromies and foliations, proving properties of Veech groups.
result Veech groups in fibers typically contain no parabolic elements.
The main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms, ranging over all surfaces. More precisely, we consider pseudo-Anosovs F:S to S with |chi(S)| log(lambda(F)) bounded above by some constant, and we prove that, after puncturing the surfaces a…
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. 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.
In this note, we mainly focus on the existence of pseudo-Einstein contact forms, an upper bound eigenvalue estimate for the CR Paneitz operator and its applications to the uniformization theorem for Sasakian space form in an embeddable closed strictly pseudoconvex CR 3-manifold. Firstly, the existence of pseudo-Einstei…
The paper studies entropy in branched covers of 3-manifolds.
problem Entropy of pseudo-Anosov monodromies in fibered 3-manifolds.
method Analyzes the minimal entropy of genus g surface bundles over the circle as 2-fold branched covers of 3-manifolds.
result There exist infinitely many 3-manifolds with comparable minimal entropy to 1/g.
We classify the pseudo-Riemannian biharmonic submersion from a 3-dimensional space form into a surface.
Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups-so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then p…
Proves unique hyperbolic metric for 3-manifolds with ideal triangulation.
problem Proving a unique hyperbolic metric for 3-manifolds with specific triangulations.
method Combining combinatorial Ricci flow with ideal triangulation for pseudo 3-manifolds.
result Extended Ricci flow converges to the hyperbolic metric exponentially fast.
Study connects flow dynamics to 3D geometry via surface intersections.
problem Relating flow dynamics to geometric properties of 3-manifolds.
method Relates pseudo-Anosov flow dynamics to hyperbolic geometry via curve graphs.
result Established a link between flow invariants and geometric features of 3-manifolds.
We establish a criterion for certain mapping classes of a surface homeomorphisms to be pseudo-Anosov in terms of the geometry of hyperbolic 3-manifolds and Gromov-hyperbolic surface group extensions. Specifically, any element of the fundamental group of a surface S gives rise to a mapping class on the punctured surface…
Characterizes transverse surfaces for pseudo-Anosov flows in 3-manifolds.
problem Characterizing surfaces transverse to pseudo-Anosov flows.
method Correspondence between surfaces and veering triangulations, Thurston norm minimization.
result Thurston-norm minimizing surfaces are almost transverse to pseudo-Anosov flows.
Study shows universal circles for taut foliations in 3-manifolds.
problem Understanding foliations in 3-manifolds.
method Analyzes pseudo-Anosov flows and taut foliations, defines universal circles.
result Action of pi_1(M) on flow space defines universal circles for taut foliations.
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.
Study on pseudo-Einstein 3-manifolds, calculating determinant changes under conformal transformations.
problem Prescribing the Q'-curvature on pseudo-Einstein 3-manifolds.
method Established an expression for the difference of determinants of Paneitz type operators under conformal changes.
result Generalized the expression of functional determinant from four to three dimensions.
Biringer, Johnson, and Minsky showed that a pseudo-Anosov map on a boundary component of an irreducible 3-manifold has a power that partially extends to the interior if and only if the (un)stable laminations of f is an R-projective limit of meridians. We prove that the power required for a pseudo-Anosov ma…
Algorithm computes Thurston norm for hyperbolic 3-manifolds.
problem Computing the Thurston norm for hyperbolic 3-manifolds.
method Developed a theory of spun-normal immersed surfaces and implemented an algorithm.
result Computed the unit ball of the Thurston norm for cusped hyperbolic 3-manifolds.
Minimal stretch factor for non-orientable surfaces is small.
problem Finding the minimal stretch factor for pseudo-Anosov homeomorphisms on non-orientable surfaces.
method Adapting Thurston's theory of fibered faces for non-orientable 3-manifolds.
result The minimal stretch factor is asymptotically on the order of 1/g.
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.
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.
Study shows universal circle isomorphic to flow space ideal boundary.
problem Understanding foliations and pseudo-Anosov flows in 3-manifolds.
method Analyzing depth-one foliations and pseudo-Anosov flows in atoroidal 3-manifolds.
result Universal circle is isomorphic to flow space ideal boundary.
The paper characterizes when a surface can be completed to a depth one lamination transverse to a pseudo-Anosov flow.
problem Characterizing when a surface can be completed to a depth one lamination transverse to a pseudo-Anosov flow.
method Homological characterization and foliation cone analysis.
result The cone of classes in H1(M\\S) that are positive on the closed orbits of φ is an entire foliation cone of M\\S. A new method computes Teichmüller polynomials from integer permutations.
problem Computing Teichmüller polynomials for fibered 3-manifolds.
method Using integer permutations to characterize pseudo-Anosov homeomorphisms and train tracks.
result Direct implementation of McMullen's algorithm for Teichmüller polynomials.
The study finds non-simple isotopy classes of links in 3-manifolds, including Legendrian and pseudo-Legendrian examples.
problem Characterizing isotopy classes of links in 3-manifolds, especially in contact structures.
method Developed theory of links transverse to a nowhere-zero vector field, constructing examples in both Legendrian and pseudo-Legendrian settings.
result Non-simple isotopy classes of links exist, including Legendrian and pseudo-Legendrian examples.
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.
We study the magic manifold N which is a hyperbolic and fibered 3-manifold. We give an explicit construction of a fiber Fa and its monodromy :Fa→Fa of the fibration associated to each fibered class a of N. Let δg (resp. δg+) be the minimal dilatation of pseudo-Anosovs (resp. pseudo-Ano…
New proof shows left orderability of 3-manifold groups with specific foliations.
problem Left orderability of 3-manifold groups with co-orientable taut foliations.
method Analyzes co-orientable taut foliations with orderable cataclysm to prove left orderability of 3-manifold fundamental groups.
result Proves left orderability of 3-manifold groups with specific foliations.
New flows represent Thurston norm ball faces, differing by veering mutations.
problem Dynamic representation of Thurston norm ball faces by distinct flows.
method Combining veering triangulations and mutations to represent faces by multiple flows.
result Non-fibered faces can be represented by two distinct flows differing by veering mutations.
Quasimorphisms and pseudo-Anosov flows
problem connections between quasimorphisms and pseudo-Anosov flows
method showing connections between quasimorphisms and pseudo-Anosov flows
result upper bounds on exponential growth rate of closed orbits in pseudo-Anosov flows
There are two objects naturally associated with a braid β∈Bn of pseudo-Anosov type: a (relative) pseudo-Anosov homeomorphism φβ:S2→S2; and the finite volume complete hyperbolic structure on the 3-manifold Mβ obtained by excising the braid closure of β, together with its braid axis, from $…
We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays exponentially in the distance form the boundary of the convex core for points in the th…
New obstructions show some 4-manifold homeomorphisms are pseudo-isotopic but not isotopic.
problem Tackling the difference between pseudo-isotopy and isotopy for 4-manifolds.
method Defining and showing realizable obstructions in Whitehead groups.
result Found homeomorphisms that are pseudo-isotopic but not isotopic.
In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant φ-sectional curvature, and prove the structure theorem for ξ-conformally fla…
The paper proves a relation between four types of invariants.
problem Proving a precise relation between four types of invariants.
method Analyzing pseudo-Anosov homeomorphisms and cusped hyperbolic 3-manifolds at roots of unity.
result A precise relation between the Baseilhac-Benedetti invariants and the Bonahon-Liu-Wong-Yang invariants.
Simon's knot genus problem solved with 3-manifold groups.
problem If epimorphism exists between knot groups, knot genus of one is greater than or equal to the other.
method Proved conjecture linking 3-manifold groups and Thurston norms, showed locally indicable groups are Lewin groups.
result Existence of epimorphism between knot groups implies knot genus inequality.
Characterizes pseudo-Anosov orbit spaces via bifoliated planes
problem Characterizing actions on bifoliated planes arising from pseudo-Anosov flows
method Using branched covers, veering triangulations, and a compactness criterion
result Extends previous work on the special case with no odd-prong singularities
Geometric methods show cosets of mapping class groups for 3-manifolds.
problem Understanding quantum representations of surface mapping class groups.
method Geometric methods and pseudo-Anosov monodromies.
result Cosets of abelian and free subgroups found in mapping class groups.