We describe a circle of ideas relating the dynamics of 2-dimensional homeomorphisms to that of 1-dimensional endomorphisms. This is used to introduce a new class of maps generalizing that of Thurston's pseudo-Anosov homeomorphisms.
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48 results for “pseudo quotient maps”
Paper shows mapping classes are largely determined by their finite quotient actions.
problem Understanding the equivalence of mapping classes based on their finite quotient actions.
method Analyzes procongruent conjugacy classes and their dependence on finite quotients.
result Procongruent conjugacy classes are largely determined by their finite quotient actions.
Study pseudo-Riemannian Sasaki metrics on solvable Lie groups.
problem Characterize and classify pseudo-Riemannian Sasaki solvmanifolds.
method Sasaki reduction and pseudo-Kähler quotient under Reeb vector field action.
result Classify pseudo-Riemannian Sasaki solvmanifolds in dimensions 5 and 7.
Thurston's fibered face theory allows us to partition the set of pseudo-Anosov mapping classes on different compact oriented surfaces into subclasses with related dynamical behavior. This is done via a correspondence between the rational points on fibered faces in the first cohomology of a hyperbolic 3-manifold and the…
Random quotients of mapping class groups have rigid properties.
problem Rigidity of random quotients of mapping class groups.
method Generalization of Ivanov's theorem and use of hierarchically hyperbolic groups.
result Automorphisms and commensurators of random quotients coincide with the groups themselves.
The paper introduces pseudo-quotients for algebraic actions and applies them to character varieties.
problem Characterizing algebraic actions and their quotients.
method Introducing pseudo-quotients as a weak version of quotients for algebraic actions, focusing on purely topological properties.
result Pseudo-quotients are unique up to virtual class in characteristic zero and can be used to compute character varieties.
New method for special generic maps into 3D space.
problem Understanding special generic maps into 3D space.
method Constructing pseudo quotient maps onto 2D polyhedra.
result Explicit construction of special generic maps into 3D space.
New examples show negative pseudo-hermitian mass and unattained CR-Sobolev quotient.
problem Negative pseudo-hermitian mass and unattained CR-Sobolev quotient in three-dimensional CR manifolds.
method Examples of compact three-dimensional CR manifolds with positive Webster class (Rossi spheres).
result First geometric context where negative pseudo-hermitian mass and unattained CR-Sobolev quotient arise.
Study of 4D symmetric spaces with (2,2) signature.
problem Existence and non-existence of compact quotients.
method Analysis of pseudo-Riemannian symmetric spaces with signature (2,2).
result Solved the problem of compact quotients existence.
We prove that some symetric semi-riemannian manifolds do not admit a proper domain which is divisible by the action of a discrete group of isometries. In other words, if a closed semi-riemannian manifold is locally isometric to such a model, and if its developing map is injective, then the manifold is actually geodesic…
The theme of this paper is that algebraic complexity implies dynamical complexity for pseudo-Anosov homeomorphisms of a closed surface S_g of genus g. Penner proved that the logarithm of the minimal dilatation for a pseudo-Anosov homeomorphism of S_g tends to zero at the rate 1/g. We consider here the smallest dilatati…
Compact quotients of homogeneous spaces are studied, leading to new findings about sphere bundles.
problem Understanding compact quotients of reductive homogeneous spaces and their implications.
method Analyzing normal bundles and sphere bundles associated with these spaces, proving homotopy triviality conditions.
result Many reductive homogeneous spaces do not admit compact quotients, resolving conjectures.
Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities.
problem Classification of continuum-wise hyperbolic surface homeomorphisms
method Proving a complete structural classification
result Every cw-hyperbolic homeomorphism is pseudo-Anosov with spine singularities
The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples of pseudo biharmonic maps will be given.
Zariski-dense deformations of standard discontinuous groups for pseudo-Riemannian homogeneous spacesmath.DG
The study explores deformations of discrete subgroups in non-compact homogeneous spaces.
problem Addressing the proper discontinuity of discrete subgroups in non-compact homogeneous spaces.
method Classification results for deformations of standard discontinuous groups in pseudo-Riemannian homogeneous spaces.
result Conditions for local rigidity and Zariski-dense deformations in standard quotients.
The study shows how quotients of mapping class groups are hierarchically hyperbolic.
problem Understanding the hierarchical hyperbolicity of mapping class groups and their quotients.
method A combinatorial criterion for hierarchical hyperbolicity applied to mapping class groups.
result Quotients of mapping class groups by large powers of Dehn twists are hierarchically hyperbolic.
Generic pseudo-Anosov mapping classes in mapping class groups.
problem Understanding the prevalence of pseudo-Anosov mapping classes.
method Proving genericity with respect to specific notions of genericity.
result Pseudo-Anosov mapping classes are generic in mapping class groups.
The paper proves Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.
problem Proving Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.
method Analyzing maps between different classes of pseudo-Hermitian manifolds, using curvature assumptions.
result Holomorphic maps are constant under certain curvature conditions.
The paper establishes Schwarz type lemmas for pseudo-Hermitian manifolds.
problem Understanding the geometry and mappings of pseudo-Hermitian manifolds.
method Using sub-Laplacian or Hessian type Bochner formulas and comparison theorems.
result Established Schwarz type results for \emph{CR} maps and transversally holomorphic maps.
Paper proves structure for compact Kähler manifolds with pseudo-effective tangent bundles.
problem Compact Kähler manifolds with pseudo-effective tangent bundles.
method Smooth or locally constant rationally connected fibration onto a quotient of a compact complex torus.
result Compact Kähler manifolds with pseudo-effective tangent bundles admit a fibration structure.
In this work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere with index s, , and having harmonic pseudo-spherical Gauss map. Then we give a characterization the…
Study quotients of curve complex actions by mapping class group.
problem Understanding actions of mapping class group on curve complex quotients.
method Cone off uniformly quasi-convex subspaces to form symmetric curve sets, non-maximal train track sets, and compression body disc sets. Analyze actions of mapping class group on these quotients.
result Actions of mapping class group on quotients are strongly WPD, non-elementary, and have infinite diameter.
Cusped spaces for hierarchically hyperbolic groups, and applications to Dehn filling quotientsmath.GT
Study of Dehn filling quotients in hierarchically hyperbolic groups.
problem Understanding the structure of Dehn filling quotients in specific groups.
method Introduced a construction for cusped spaces of relatively hyperbolic groups and used it to study Dehn-filling-like quotients.
result Infinite hyperbolic quotients of mapping class groups of punctured spheres and braid groups are found.
Meta-nilpotent quotients of mapping-torus groups and two topological invariants of quadratic formsmath.GT
Study centers of mapping-torus groups to define knot and mapping class invariants.
problem Understanding the center of mapping-torus groups.
method Determine the center of meta-nilpotent quotients of mapping-torus groups.
result Introduce two invariants of knots and mapping classes as quadratic forms.
The paper explores mapping class group quotients by Dehn twists and their representations.
problem Finite quotients and representations of mapping class groups by powers of Dehn twists.
method Construction of finite quotients using representations with Zariski dense images into semisimple Lie groups, and Long and Moody's method.
result The Fibonacci TQFT representation is a specialization of the Jones representation in genus 2.
In this paper, we give an estimate of sub-Laplacian of Riemannian distance functions in pseudo-Hermitian geometry which plays a similar role as Laplacian comparison theorem in Riemannian geometry, and deduce a prior horizontal gradient estimate of pseudo-harmonic maps from pseudo-Hermitian manifolds to regular balls of…
New family of measurable pseudo-Anosov maps on spheres.
problem Generalizing pseudo-Anosov maps to measurable ones.
method Continuous family of homeomorphisms on sphere, semi-conjugate to core tent map.
result Measurable pseudo-Anosov maps have invariant dense streamlines with uniform measures.
In this paper, we derive the second variation formula of pseudoharmonic maps into any pseudo-Hermitian manifolds. When the target manifold is an isometric embedded CR manifold in complex Euclidean space or a pseudo-Hermitian immersed submanifold in Heisenberg group, we give some conditions on Weingarten maps to obtain …
Paper translates train track concepts to cluster algebras for pseudo-Anosov mapping classes.
problem Understanding pseudo-Anosov mapping classes on surfaces.
method Using Goncharov--Shen's potential function, the paper translates train track concepts into cluster algebra language.
result Proves sign stability of general pseudo-Anosov mapping classes.
In this paper, we discuss the heat flow of a pseudo-harmonic map from a closed pseudo-Hermitian manifold to a Riemannian manifold with non-positive sectional curvature, and prove the existence of the pseudo-harmonic map which is a generalization of Eells-Sampson's existence theorem. We also discuss the uniqueness of th…
The study examines power quotients of surface groups and mapping class groups, proving structural properties and isomorphisms.
problem Structural properties and isomorphisms of power quotients of surface groups and mapping class groups.
method Analyzes the outer automorphism and automorphism groups of power quotients, proving isomorphisms and structural properties.
result The outer automorphism group of is isomorphic to the quotient of the extended mapping class group of by th powers of Dehn twists.
The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.
problem Analyzing maps between pseudo-Hermitian and Kähler manifolds.
method Investigates partial energy functionals and critical maps, proving foliated results for - and -harmonic maps.
result Generalizes Siu's holomorphicity result to - and -harmonic maps.
Construct pseudo-Anosovs from expanding interval maps, reconciling Thurston's construction.
problem Constructing pseudo-Anosov homeomorphisms from expanding interval maps.
method Classifying circumstances for constructing pseudo-Anosovs from a specific subclass of generalized pseudo-Anosovs.
result Produces pseudo-Anosovs on surfaces of genus with algebraically primitive translation structures and Salem dilatations.
Characterizes pseudo-Anosov mapping classes using cluster algebra techniques.
problem Characterize pseudo-Anosov mapping classes purely in terms of shear coordinates.
method Uses cluster algebraic generalization and tropical cluster transformations.
result Algebraic entropies of cluster transformations match topological entropy.
Investigates intrinsic Lipschitz sections in nonlinear quotient maps.
problem Analyzing intrinsic Lipschitz sections in non-linear quotient maps.
method Introduced Leibniz formula for intrinsic slope under weaker conditions, used properties of intrinsic dilations in Carnot groups, and provided conditions for sum of sections.
result Found conditions for sum of intrinsically Lipschitz sections in Carnot groups of step 2.
The aim of our paper is to construct pseudo -type algebras from the covering free nilpotent two-step Lie algebra as the quotient algebra by an ideal. We propose an explicit algorithm of construction of such an ideal by making use of a non-degenerate scalar product. Moreover, as a bypass result, we recover the existe…
Metric WPD for pseudo-Anosov maps shows many unbounded quasi-morphisms.
problem Understanding quasi-morphisms on pseudo-Anosov maps.
method Metric weak proper discontinuity (WPD) for pseudo-Anosov maps.
result Existence of many unbounded quasi-morphisms on homeomorphisms with large fixed sets.
Study Agol cycles for pseudo-Anosov 3-braids.
problem Conditions for equivalent Agol cycles of pseudo-Anosov 3-braids.
method Investigate necessary and sufficient conditions.
result Necessary and sufficient conditions for equivalent Agol cycles of pseudo-Anosov 3-braids.
Study on measurable pseudo-Anosov maps on surfaces.
problem Characterize dynamics of pseudo-Anosov maps on surfaces.
method Analyze measurable pseudo-Anosov homeomorphisms with specific properties.
result Prove transitivity, dense periodic points, sensitivity, and ergodicity.
The study examines translation lengths of pseudo-Anosov maps on curve graphs.
problem Estimating translation lengths of pseudo-Anosov maps on curve graphs.
method Analyzing geodesic axes and powers of Dehn twists.
result Determining minimal translation lengths and optimizing map ratios.
Study compares Kähler quotients of torus actions under varying moment maps.
problem Comparing Kähler quotients of torus actions under varying moment maps.
method Analyzes the transformation of Kähler quotients as moment maps change, proving bimeromorphic transformations and desingularizations.
result Each nondegenerate singular Kähler quotient has a partial and rational desingularization.
We study types of mapping classes which arise as a product of a given mapping class and powers of certain pure mapping classes. We derive an explicit constant depending only on a surface such that almost all above pure mapping classes give rise to pseudo-Anosov type whenever their powers are larger than the constant. F…
We show that an orientable pseudo-Anosov homeomorphism has vanishing Sah-Arnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal. We relate this to works of Margalit-Spallone and Birman, Brinkmann and Kawamuro. Mainly, we use Veech's construction of pseudo-Anosov maps to give ex…
We show that any pseudo-Anosov map that is a lift of pseudo-Anosov homeomorphism of a nonorientable surface has vanishing SAF invariant. We also provide a criterion to certify that a pseudo-Anosov map is not such a lift.
The paper finds pseudo-Anosov-like maps on an infinite ladder surface.
problem Exploring dynamics on infinite surfaces.
method Lifts Penner-type pseudo-Anosov maps from a closed surface to an infinite ladder surface.
result Existence and properties of pseudo-Anosov-like maps on the infinite ladder surface.
We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R^m into a pseudo-Riemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point i…
In the first part of this paper we prove that the mapping class subgroups generated by the -th powers of Dehn twists (with ) along a sparse collection of simple closed curves on an orientable surface are right angled Artin groups. The second part is devoted to power quotients, i.e. quotients by the normal s…
New findings on generating mapping class groups using pseudo-Anosov elements.
problem Generating mapping class groups using specific types of elements.
method Proving the generation of mapping class groups by pseudo-Anosov elements and conjugate reducible but not periodic elements.
result The mapping class group can be generated by two conjugate pseudo-Anosov elements with arbitrarily large dilatations for surfaces of genus greater than or equal to nine.