Taut foliations map leaves to branched 2-sphere covers.
problem Understanding taut foliations in 3-manifolds.
method Map foliation leaves to branched 2-sphere covers.
result Taut foliations are characterized by such maps.
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48 results for “branching foliations”
Left orderability proven for certain 3-manifolds with specific foliations.
problem Proving left orderability for specific 3-manifolds with taut foliations.
method Analyzing the fundamental group of a 3-manifold with a co-orientable taut foliation.
result The fundamental group of the 3-manifold is left orderable.
We study the question of when cyclic branched covers of knots admit taut foliations, have left-orderable fundamental group, and are not L-spaces.
A formula calculates the Euler class of foliations using dual graphs.
problem Calculating the Euler class of foliations using cooriented branched surfaces.
method Using dual graphs of cooriented branched surfaces to define a simplicial 1-cycle representing the Poincaré dual of the Euler class.
result The formula generalizes previous results and classifies realizable homology classes.
We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the local existence and uniqueness results which hold for genuine surfaces. Moreover…
Simplified proof of a theorem about 3D shapes.
problem Proving a theorem about foliations on 3-manifolds.
method Using foliated branched covers.
result A simple proof of Novikov's theorem.
We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred knots in integer homology -spheres and cyclic branched covers of closed braids. The latter allows us to complete the proof…
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 laminations come from a universal circle, a refinement of the universal circles pro…
Study partially hyperbolic diffeomorphisms in 3D, focusing on foliations and dynamics.
problem Classify 3D partially hyperbolic diffeomorphisms homotopic to the identity.
method Analyze Burago and Ivanov's branching foliations in Seifert fibered and hyperbolic manifolds.
result Complete classification of diffeomorphisms in Seifert fibered manifolds, and new potential class in hyperbolic manifolds.
We define a norm on the homology of a foliated manifold, which refines and majorizes the usual Gromov norm on homology. This norm depends in an upper semi-continuous way on the underlying foliation, in the geometric topology, and can therefore be used to study the question of which foliations arise as geometric limits …
Earlier we introduced and studied the concept of holomorphic {\it branched Cartan geometry}. We define here a foliated version of this notion; this is done in terms of Atiyah bundle. We show that any complex compact manifold of algebraic dimension admits, away from a closed analytic subset of positive codimension, …
Paper proves S-stability of foliations on flow-spines with transverse Reeb flow.
problem Characterizing S-stable foliations on flow-spines with transverse Reeb flow.
method Introduced S-stability for foliations on branched simple polyhedrons and proved stability for 1-forms with .
result Proved the number of simple tangency points of an S-stable foliation on a flow-spine is at least 2.
Survey on holomorphic structures on complex manifolds.
problem Holomorphic foliations with transverse holomorphic Cartan geometries.
method Analyzes G-structures and Cartan geometries on compact complex manifolds.
result Foliated holomorphic Cartan geometries on compact complex manifolds.
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.
New method finds unique branched surfaces in 3-manifolds.
problem Finding unique branched surfaces in 3-manifolds.
method Proving endperiodic maps have periodic splitting sequences.
result Veering branched surfaces are unique up to equivalence.
We consider triangulations of closed surfaces S with a given set of vertices V; every triangulation can be branched that is enhanced to a Delta-complex. Branched triangulations are considered up to the b-transit equivalence generated by b-flips (i.e. branched diagonal exchanges) and isotopy keeping V point-wise fixed. …
Let be a leafwise hyperbolic taut foliation of a closed 3-manifold and let be the leaf space of the pullback of to the universal cover of . We show that if has branching, then the natural action of on is faithful. We also show that if has a finite branch locus whose stabilize…
The article proves properties of Seifert links and their cyclic branched covers.
problem Properties of Seifert links and their cyclic branched covers.
method Left-orderability, co-oriented taut foliations, and -space properties.
result Proves the link conjecture for Seifert links.
We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex multiplicities (in the multivalued ''Darboux'' case). We specify normal forms in e…
Approximations of foliationsmath.GT
Suppose that is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that has continuous tangent plane field and is {\sl taut}; that is, closed smooth transversals to pass through every point of . We show that if $\mathcal…
New foliations constructed from contact pairs, revealing flexible taut foliations.
problem Characterizing taut foliations in 3D.
method Construction of codimension-one foliations from pairs of contact structures in 3D.
result Foliations constructed are taut, providing new insights into the L-space conjecture.
The paper proves left-orderability for certain Dehn fillings of pseudo-Anosov mapping tori.
problem Left-orderability of fundamental groups in Dehn fillings of pseudo-Anosov mapping tori.
method Two approaches: one using -covered foliations and the other using one-sided branching.
result All such Dehn fillings have left-orderable fundamental groups.
In this article we study the topological structure of the lifts to the universal of the stable and unstable foliations of -dimensional Anosov flows. In particular we consider the case when these foliations do not have Hausdorff leaf space. We completely determine the structure of the set of non separated leaves from…
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 continuously to the sphere at infinity, hence the limit sets are continuous images of…
Detect slopes in toroidal 3-manifolds to prove properties of fundamental groups.
problem Prove properties of fundamental groups of toroidal 3-manifolds.
method Slope detection using left-orders, foliations, and Heegaard Floer homology.
result Toroidal integer homology spheres have left-orderable fundamental groups.
We prove the existence of foliations transverse to pseudo-Anosov flows using veering triangulations.
problem Existence of foliations transverse to pseudo-Anosov flows in 3-manifolds.
method Combinatorial approach via veering triangulations and branched surfaces.
result Existence of transverse foliations for certain pseudo-Anosov flows.
Let N be a manifold (with boundary) of dimension at least 3, such that its interior admits a hyperbolic metric of finite volume. We discuss the possible limits arising from sequences of relative fundamental cycles approximating the simplicial volume. As applications, we extend results of Jungreis and Calegari from clos…
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.
A knot in is persistently foliar if, for each non-trivial boundary slope, there is a co-oriented taut foliation meeting the boundary of the knot complement transversely in a foliation by curves of that slope. For rational slopes, these foliations may be capped off by disks to obtain a co-oriented taut foliati…
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.
Analytic patch trees reveal new geometric structures and dimension fields.
problem Understanding the geometric and analytical properties of surface patch trees.
method Developed analytic surface patch trees and introduced interface curves to transmit state.
result Surface patch trees have natural foliations with one-dimensional curve trees and dimension fields.
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
Paper tackles -space conjecture for knot manifolds, proving equivalence for some properties.
problem Tackles -space conjecture for knot manifolds, proving equivalence for some properties.
method Introduces relative -space conjecture, characterizes slope detection, uses Heegaard Floer homology, left-orders, and foliations.
result Confirms equivalence of and for slope detected knots, identifies exceptional slopes.
Maps links in 3-manifolds to links in branched covers, relating quantum field theories.
problem Understanding defects in quantum field theories and their relationships.
method Using -nonabelianization to map links in 3-manifolds to branched covers, relating UV and IR theories.
result Computes Jones polynomial and protected spin characters for BPS states.
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 between stable and unstable leaves and the flow is not topologically conjugate to …
Using twistor methods, we explicitly construct all local forms of four--dimensional real analytic neutral signature anti--self--dual conformal structures with a null conformal Killing vector. We show that is foliated by anti-self-dual null surfaces, and the two-dimensional leaf space inherits a natural pr…
Study on moduli spaces of branched projective structures on surfaces.
problem Characterizing and understanding moduli spaces of branched projective structures.
method Analytic and geometric methods to study the moduli spaces of branched projective structures.
result The moduli space of marked branched projective structures is a complex analytic space with specific dimensions and singular points.
We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, whi…
We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are…
New criterion for branched covers between 2-spheres.
problem Existence of specific types of branched covers between 2-spheres.
method Combining complex analysis and topology techniques.
result Established a complete criterion for the existence of branched covers.
Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected close surface N with Euler's characteristic less than or equal to 0. This …
Uniformly branching treesmath.CV
Uniformly branching trees are equivalent to certain metric spaces.
problem Characterizing metric spaces equivalent to uniformly branching trees.
method Proving equivalence between trivalent quasiconformal trees and uniformly branching trees.
result Any two uniformly branching trees are quasisymmetrically equivalent.
The paper studies which branched covers can be lifted to braided embeddings.
problem Which branched covers lift to braided embeddings?
method Analyzes conditions for liftability using Hansen's criterion and examples in different dimensions.
result Not all branched covers lift to braided embeddings; examples are provided in various dimensions.
We consider 3-dimensional pseudo-manifolds M with a given set of marked point V such that M-V is the interior of a compact 3-manifold with boundary. An ideal triangulation T of (M, V ) has V as its set of vertices. A branching (T, b) enhances T to a Delta-complex. Branched triangulations of (M, V ) are considered up to…
The paper details folding of branched covers of the 3-sphere over knots.
problem Understanding folding of branched covers of the 3-sphere over knots.
method Presenting detailed foldings of dihedral covers of the 3-sphere branched over torus knots.
result Detailed foldings of dihedral covers of the 3-sphere branched over torus knots are presented.
In this work we characterize branch data of branched coverings of even degree over the projective plane which are realizable by indecomposable branched coverings.
Course on knots using branched coverings.
problem Determining knots using cyclic branched coverings.
method Cyclic branched coverings of knots.
result New insights into knot classification.
New method learns better branching policies for MILP problems.
problem Improving branch and bound search for solving MILP problems.
method Imitates strong branching rule with parameterized state of B&B search tree.
result Generalized policies outperform current state-of-the-art.