Unified proof of Nielsen-Thurston classification via Teichmüller's theorem.
problem Classifying mapping class groups and rational maps.
method Unified proof following Bers' approach.
result Unified proof of Nielsen-Thurston classification.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Thurston classification”
Classifies elements of cluster modular groups into three types.
problem Classifying elements of cluster modular groups.
method Characterizes elements in terms of fixed points on tropical compactifications.
result Analogous to Nielsen-Thurston classification theory.
Paper classifies 5D Thurston geometries, finding an uncountable family.
problem Classifying 5-dimensional Thurston geometries.
method Summarizes the general classification, providing a full list and examples.
result An uncountable family of geometries discovered.
Classification of Legendrian knots of topological type with maximal Thurston--Bennequin numbermath.GT
Classifies Legendrian knots with maximal Thurston-Bennequin number.
problem Classifying Legendrian knots of a specific type.
method Using Thurston-Bennequin number as a criterion.
result Confirms conjectures about Legendrian knots of type .
The paper classifies hypersurfaces in a specific 4D geometry.
problem Classify homogeneous hypersurfaces in the four-dimensional Thurston geometry .
method Used geometric conditions to classify hypersurfaces with constant principal curvatures.
result Complete classification of homogeneous hypersurfaces in .
This book explains Thurston's geometrization of 3-manifolds.
problem Understanding the geometry and topology of 3-manifolds.
method Detailed explanations of geometric and topological concepts.
result Thurston's geometrization theorem proved by Perelman.
Study of homeomorphisms on infinite type surfaces with a classification theorem.
problem Classifying homeomorphisms on surfaces of infinite type.
method Introduce tame homeomorphisms and prove a Nielsen-Thurston type classification theorem.
result For tame homeomorphisms, surfaces decompose into invariant subsurfaces with canonical decompositions.
For each fixed n>=2 we show how the Nielsen-Thurston classification of mapping classes for a closed surface of genus g>=2 is determined by the sequence of quantum SU(n) representations, when one considers all levels. That this is the case is a consequence of our asymptotic faithfulness property. We here provide explici…
Explains Thurston geometries and visualization techniques.
problem Classifying Thurston geometries and their visualization.
method Survey of history and recent techniques.
result Discussion of recent immersive visualization techniques.
Proof of surface homeomorphism classification theorem.
problem Classify homeomorphisms of surfaces of finite type.
method Neilsen-Thurston classification theorem proof.
result Proof of Nielsen-Thurston theorem for surfaces of finite type.
The paper classifies homogeneous hypersurfaces in three 4D Thurston geometries.
problem Classifying homogeneous hypersurfaces in specific 4D geometries.
method Analyzing isometry groups and applying classification techniques.
result Homogeneous hypersurfaces identified in , and .
The paper compactifies stability conditions on curves, akin to Teichmüller theory.
problem Compactifying spaces of stability conditions on curves.
method Constructing a Thurston-like compactification.
result Obtained a compactification of stability conditions space, analogous to Teichmüller theory.
Thurston obtained a classification of individual surface homeomorphisms via the dynamics of the corresponding mapping class elements on Teichmüller space. In this paper we present certain extended versions of this, first, to random products of homeomorphisms and second, to holomorphic self-maps of Teichmüller spaces.
We show that the Nielsen-Thurston classification of mapping classes of the sphere with four marked points is determined by the quantum SU(n)-representations, for any fixed integer . In the Pseudo-Anosov case we also show that the stretching factor is a limit of eigenvalues of (non-unitary) SU(2)-TQFT represen…
In this article, we propose two algorithms for determining the Nielsen-Thurston classification of a mapping class on a surface . We start with a finite generating set for the mapping class group and a word in . We show that if represents a reducible mapping class in $\Mod(S)$ then …
We study the action of the elements of the mapping class group of a surface of finite type on the Teichmüller space of that surface equipped with Thurston's asymmetric metric. We classify such actions as elliptic, parabolic, hyperbolic and pseudo-hyperbolic, depending on whether the translation distance of such an elem…
We study the action of the mapping class group on the real homology of finite covers of a topological surface. We use the homological representation of the mapping class to construct a faithful infinite-dimensional representation of the mapping class group. We show that this representation detects the Nielsen-Thurston …
Homogeneous Hypersurfaces in 4-dimensional Thurston Geometries with 4-dimensional Isometry Groupmath.DG
Classifies homogeneous hypersurfaces in specific 4D geometries.
problem Classifying homogeneous hypersurfaces in 4D Thurston geometries.
method Analyzing subalgebras of Lie algebras and isometry groups.
result Determined all homogeneous hypersurfaces up to ambient isometries.
New classification for Vaisman manifolds with specific properties.
problem Classifying Vaisman manifolds with large first Betti number and vanishing first basic Chern class.
method Analyzing properties and using diffeomorphism and complex structure invariance.
result Every Vaisman manifold with large first Betti number and vanishing first basic Chern class is diffeomorphic to a Kodaira-Thurston manifold.
Study of hypersurfaces in Sol4_0 geometry, classifying parallel and totally umbilical types.
problem Classifying hypersurfaces in the Sol4_0 geometry.
method Analyzing hypersurfaces with Codazzi tensors and parallel second fundamental forms.
result Full classification of hypersurfaces in Sol4_0, including parallel and totally umbilical types.
The paper classifies Legendrian and transverse knots in cable knot types.
problem Classifying Legendrian and transverse knots in specific knot types.
method Using the classification of the underlying knot and new phenomena of 'Legendrian large' cables.
result Criteria for classifying Legendrian and transverse knots in negative cables.
Problems of knot classification and manifold properties are shown to be NP-complete.
problem Determining knot non-triviality and Thurston norm in 3-manifolds.
method NP-completeness proofs for specific problems in knot theory and 3-manifold topology.
result Problems of knot classification and manifold properties are proven to be NP-complete.
Study shows certain diffeomorphisms cannot be dynamically coherent.
problem Dynamically coherent behavior in partially hyperbolic diffeomorphisms.
method Analyzes pseudo-Anosov components and Nielsen-Thurston classification.
result Extends previous work to larger class of diffeomorphisms.
Study of harmonic Riemannian submersions from 3D geometries.
problem Characterizing harmonic Riemannian submersions from specific 3D geometries.
method Using generalized integrability data and classifications of Thurston's 3D geometries, 3D BCV spaces, and Berger sphere.
result Complete classifications and explicit constructions of harmonic Riemannian submersions.
We classify pairs where is a --dimensional simply connected smooth manifold and a Lie group acting on transitively, effectively with compact isotropy group.
Classifies 5D homogeneous geometries with specific isotropy properties.
problem Classifying 5D homogeneous geometries with certain isotropy properties.
method Thurston's classification of homogeneous geometries, focusing on irreducible and trivial isotropy representations.
result Identifies 5D geometries with irreducible isotropy as irreducible Riemannian symmetric spaces and those with trivial isotropy as specific solvable Lie groups.
We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and Thurston, except an automorphism of a reducible manifold must first be written as…
Classifies 5D homogeneous geometries with nontrivial reducible linear isotropy.
problem Classifying 5D homogeneous geometries with specific properties.
method Thorough classification using Thurston's criteria and analysis of linear isotropy representations.
result Found a countably infinite family of geometries diffeomorphic to .
Survey on Thurston metric on Teichmüller space, focusing on extremal maps.
problem Constructing extremal Lipschitz maps between hyperbolic surfaces.
method Review of constructions including Thurston's original work.
result Coarse geometry and isometry rigidity of Thurston metric discussed.
In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least different Legendrian representatives with maximal Thurston--Bennequin number of the twist knot with crossing number . In t…
We prove a conjecture due to Makanin: if a and b are elements of the Artin braid group B_n such that a^k=b^k for some nonzero integer k, then a and b are conjugate. The proof involves the Nielsen-Thurston classification of braids.
The paper extends Thurston's method to new variants of Mather-Thurston theorem.
problem Proving new variants of Mather-Thurston theorem for PL homeomorphisms and contactomorphisms.
method Generalizing Thurston's technique to prove new variants of Mather-Thurston theorem for PL homeomorphisms and contactomorphisms.
result The paper answers questions posed by Gelfand-Fuks and Greenberg on PL foliations and Rybicki on contactomorphisms.
Developed theory for Thurston maps with a small set of essential singularities.
problem Characterizing Thurston maps with essential singularities.
method Analyzed pullback maps on Teichmüller space to characterize Thurston maps.
result Established a characterization theorem for Thurston maps with four postsingular values.
Study of Thurston's Master Teapot and its properties.
problem Characterize geometric and topological properties of Thurston's Master Teapot.
method Establish basic geometric and topological properties through analysis of self-maps and intersections.
result The Master Teapot is connected, contains the unit cylinder, and its intersection with grows monotonically with .
We discuss existence and classification of totally umbilic surfaces in the model geometries of Thurston and the Berger spheres. We classify such surfaces in , and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.
The study classifies biharmonic submersions from 3D BCV spaces.
problem Classifying biharmonic submersions from 3D BCV spaces.
method Complete classification through proving existence and constructing families of submersions.
result Proper biharmonic Riemannian submersions exist only in two specific cases.
Article explores Thurston's circle packing theorem in 3-manifold geometry.
problem Understanding Thurston's circle packing theorem in 3-manifold geometry.
method Analyzes the Koebe-Andre'ev-Thurston Theorem and its relation to Thurston's circle packing theorem.
result Illustrates the significance of Thurston's circle packing theorem in 3-manifold geometry.
Algorithm classifies surface homeomorphisms with polynomial time complexity.
problem Classifying surface homeomorphisms with polynomial time complexity.
method Algorithm to compute curve distances and decide Nielsen-Thurston types.
result Polynomial time classification of surface homeomorphisms.
Overview of Thurston's work in math.
problem None explicitly stated, focuses on Thurston's contributions.
method Presentation of significant results.
result Impact of Thurston's work on mathematics.
New method constructs symplectic structures on 4-manifolds from trisections.
problem Characterize 4-manifolds admitting symplectic structures.
method Explicit criteria on trisections allow construction of symplectic structures.
result New characterization of 4-manifolds with symplectic structures.
We correct and complete a conjecture of D. Gabai, R. Meyerhoff and N. Thurston on the classification and properties of thin tubed closed hyperbolic 3-manifolds. We additionally show that if N is a closed hyperbolic 3-manifold, then either N=Vol3 or N contains a closed geodesic that is the core of an embedded tube of ra…
Study shows genus two Heegaard diagrams for all Thurston geometries.
problem Finding Heegaard diagrams for Thurston geometries.
method Collecting genus two Heegaard diagrams for all eight Thurston geometries.
result Each Thurston geometry has a genus two Heegaard example.
Uniformly finite Cannon--Thurston fibers in most hyperbolic settings.
problem Existence and finiteness of Cannon--Thurston maps.
method Analysis of proper maps between hyperbolic metric spaces.
result Uniform finiteness of Cannon--Thurston fibers in most known settings.
In earlier work, we had shown that Cannon-Thurston maps exist for Kleinian surface groups. In this paper we prove that pre-images of points are precisely end-points of leaves of the ending lamination whenever the Cannon-Thurston map is not one-to-one. In particular, the Cannon-Thurston map is finite-to-one. This comple…
We show that Cannon-Thurston maps exist for degenerate free groups without parabolics, i.e. for handlebody groups. Combining these techniques with earlier work proving the existence of Cannon-Thurston maps for surface groups, we show that Cannon-Thurston maps exist for arbitrary finitely generated Kleinian groups witho…
Study on Thurston norms of specific 3-manifolds with two generators and one relator.
problem Understanding the complexity of surfaces in 3-manifolds with specific properties.
method Analyzing Thurston norms of 3-manifolds with two generators and one relator, focusing on their unit balls and faces.
result Found 3-manifolds with unit balls of Thurston norms having arbitrarily many faces.
New biharmonic functions found on Thurston geometries.
problem Finding biharmonic functions on Thurston geometries.
method Constructing explicit proper biharmonic functions.
result Explicit biharmonic functions constructed on various Thurston geometries.
Historical notes on Thurston's 3-manifold geometry.
problem Exploring Thurston's notes on 3-manifold geometry.
method Historical commentary and references.
result Discussion of Lobachevsky, Andreev, and Milnor's works.