Survey on affine Anosov representations and their implications.
problem Generalizing Anosov representations to affine settings.
method Discussion and survey of existing work.
result Implications of affine Anosov representations.
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48 results for “Affine Anosov representations”
New definitions and properties for hyperbolic group representations.
problem Understanding representations of hyperbolic groups into affine groups.
method Defining affine Anosov representations and proving their equivalence to Anosov linear parts with proper action.
result Affine Anosov representations of hyperbolic groups have specific properties related to their linear parts and proper actions.
The paper defines cocycles for positive Anosov representations and constructs affine actions with bounded fundamental domains.
problem Positive Anosov representations into .
method Definition of cocycles and construction of affine actions with fundamental domains.
result Quotient manifolds are homeomorphic to handlebodies.
Study on Hausdorff dimension of Anosov subgroup limit sets under specific affine complexity.
problem Investigating the Hausdorff dimension of Anosov subgroup limit sets with self-affine complexity.
method Analyzing the Hausdorff dimension of projective limit sets of Anosov subgroups under specific assumptions about their affine complexity.
result The Hausdorff dimension of is determined by the critical exponent of the first simple root under partial quasi-self-similarity.
The paper studies Anosov holonomy groups in complete affine manifolds.
problem Characterizing Anosov holonomy groups in complete affine manifolds.
method Representation theory and coarse geometry techniques.
result Complete affine manifolds with Anosov holonomy groups have specific geometric properties.
Affine actions fail for Hitchin linear parts, except flat pseudo-Riemannian cases.
problem Properly discontinuous affine actions of surface groups with Hitchin linear part.
method Analysis of representations and pseudo-Riemannian metrics.
result Hitchin linear parts in lead to non-properly discontinuous affine actions.
On the dimension of limit sets on via stationary measures: variational principles and applicationsmath.DS
The paper studies the dimension of limit sets using variational principles and stationary measures.
problem Calculating the Hausdorff dimension of limit sets of Anosov representations and the Rauzy gasket.
method Established variational principles for affinity exponents and Rauzy gaskets, combined with dimension formulas of stationary measures.
result Yields the equality between the Hausdorff dimensions and affinity exponents in both settings.
The paper defines conditions for proper actions and relates them to Margulis spacetimes.
problem Understanding proper actions on specific geometric spaces.
method Analyzes Anosov representations and their infinitesimal versions.
result Interprets Margulis spacetimes as quotient manifolds of .
In this paper, we show that a compact affine manifold endowed with an Affine Anosov transformation is finitely covered by a complete affine nilmanifold.
Partially hyperbolic flows on flat vector bundles with an application to complete affine manifoldsmath.GT
Study partially hyperbolic flows on flat bundles, proving equivalence for complete affine manifolds.
problem Characterize partially hyperbolic representations of fundamental groups of manifolds.
method Representation theory techniques, focusing on holonomy representations and their properties.
result Show equivalence between partially hyperbolic representations and -Anosov representations for complete affine manifolds.
Proves nonemptyness of domains for specific group actions.
problem Nonemptyness of domains of proper discontinuity for Anosov groups of affine Lorentzian transformations.
method Proof of nonemptyness of domains of proper discontinuity.
result Proves nonemptyness of domains for Anosov groups of affine Lorentzian transformations.
The study limits the cohomological dimension of certain affine manifolds with partially hyperbolic holonomy groups.
problem Understanding cohomological dimensions of affine manifolds with specific holonomy groups.
method Analyzing the tangent bundle structure and using coarse geometry techniques.
result The cohomological dimension is bounded by the dimension minus the index of the holonomy group.
We show that sufficiently irreducible Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.
We show that sufficiently irreducible totally non-symplectic Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.
The paper explores Anosov flows on torus bundles and provides new insights.
problem Investigating Anosov flows on affine torus bundles and their properties.
method Surgery type construction of Anosov flows and dichotomy result for fiberwise Anosov flows.
result New insights into Anosov flows, including non-transitive flows in odd dimensions.
Study Anosov representations of reducible suspensions of hyperbolic groups.
problem Characterize dynamical properties of reducible suspensions of Anosov representations.
method Analyzing linear representations of non-elementary hyperbolic groups, focusing on weak unipotent actions on subspaces.
result Characterize when reducible suspensions are discrete and faithful, quasi-isometrically embedded, and Anosov.
Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groupsmath.DG
Develops theory of Anosov representations for Fuchsian groups, showing stability and analytical properties.
problem Understanding geometrically finite Fuchsian groups and their representations.
method Theory of Anosov representations, type-preserving deformations, limit maps, relative Anosov and dominated representations.
result Cusped Hitchin representations are Borel Anosov, stable under deformations, and limit maps vary analytically.
Develops theory of relatively Anosov representations using flow examples.
problem Understanding relatively Anosov representations.
method Uses a contracting flow on a bundle to define Anosov representations and builds examples.
result Builds families of examples of relatively Anosov representations.
Survey on geometry of co-Minkowski space and its affine deformations.
problem Understanding the geometry of co-Minkowski space and its affine deformations.
method Affine deformations of hyperbolic lattices acting on co-Minkowski space, convex core, mean hypersurface, asymmetric norm.
result Existence of a unique mean hypersurface and an asymmetric norm on the space of affine deformations.
Characterizes groups for specific types of representations into SL(d,R).
problem Understanding groups admitting certain types of representations into SL(d,R).
method Characterization and bounds on cohomological dimension.
result Bounds on cohomological dimension and characterizations of representations.
Study of infinite hyperbolic surfaces and their automorphisms.
problem Behavior of hyperbolic affine automorphisms on infinite translation surfaces.
method Analysis of dynamics, mixing properties, and polynomial decay.
result Hyperbolic affine automorphisms are not recurrent but have mixing properties.
New representations for surface groups expand known Anosov classes.
problem Understanding new types of representations for surface groups.
method Introducing and studying simple Anosov representations of closed hyperbolic surface groups.
result Simple Anosov representations strictly contain Anosov representations.
New findings on cusped Borel Anosov representations and their properties.
problem Characterizing and understanding cusped Borel Anosov representations.
method Analyzing representations of lattices in to .
result Cusped Borel Anosov representations with specific properties are Hitchin representations.
Characterizes Anosov reducible representations in terms of eigenvalues.
problem Understanding Anosov representations in reducible settings.
method Characterizes Anosov representations using eigenvalue magnitudes of irreducible block factors.
result Connected components of character varieties do not contain reducible representations for many non-elementary hyperbolic groups.
Study of flows on complex manifolds with holomorphic properties.
problem Global rigidity of transversely holomorphic Anosov flows on smooth compact manifolds.
method Analyzing the integrability of unstable and stable distributions, proving uniqueness in low dimensions.
result For topologically transitive flows, they are either orbit equivalent to a hyperbolic automorphism or geodesic flow.
New domains of discontinuity found for Anosov representations.
problem Understanding Anosov representations acting on homogeneous spaces.
method Constructing open domains of discontinuity for Anosov representations acting on specific homogeneous spaces.
result Describes the largest possible open domains of discontinuity for Zariski dense Anosov representations.
Paper defines conditions for limit sets of Anosov representations to be smooth submanifolds.
problem Understanding the smoothness of limit sets of Anosov representations.
method Established conditions for limit sets to be differentiable submanifolds and calculated optimal Holder constants.
result Limit sets of projective Anosov representations are differentiable submanifolds with Holder continuous derivatives.
Theory of relatively Anosov representations using flow methods.
problem Developing a theory for relatively Anosov representations.
method Using the contracting flow on a bundle to define and study relatively Anosov representations.
result Definition and study of uniformly relatively Anosov representations and a stability result.
Maximal and Borel Anosov representations in are proven to be Hitchin.
problem Characterizing representations of surface groups into that are Borel Anosov and maximal.
method Proving representations are Hitchin if they have maximal Toledo invariant and are Borel Anosov.
result Maximal and Borel Anosov representations in are Hitchin.
Identifies Anosov representations of hyperbolic triangle groups in SL(3,R).
problem Classifying Anosov representations of hyperbolic triangle groups into SL(3,R).
method Proving representations are Anosov if they lie in the Hitchin component or the Barbot component, with specific conditions for eigenvalues.
result Anosov representations in SL(3,R) have non-convex boundary maps.
New representations defined for groups and graphs, with applications to stable representations.
problem Defining and constructing new types of representations for groups and graphs.
method Introducing -directed Anosov representations and using Fock-Goncharov positivity to construct them.
result Constructs large families of primitive stable representations from to , including non-discrete and non-faithful examples.
Cube complexes allow hyperbolic groups to have Anosov representations.
problem Understanding representations of hyperbolic groups in higher dimensions.
method Analyzing representations of hyperbolic groups acting on CAT(0) cube complexes.
result Generic representations of certain groups are Anosov.
The paper introduces cataclysm deformations for Anosov representations.
problem Deforming Anosov representations in Lie groups.
method Constructing cataclysm deformations for -Anosov representations into semisimple Lie groups.
result Cataclysm deformations are injective for Hitchin representations but not for all -Anosov representations.
New representation theory for closed geodesic subflows.
problem Classifying representations with good geometric properties.
method Restricting to invariant closed geodesic subflows.
result Equivalent characterizations and properties of new representations.
The paper constructs Anosov representations for specific types of groups.
problem Constructing Anosov representations for certain groups.
method Analyzing uniform lattices and their extensions, proving existence of Anosov embeddings.
result Examples of one-ended hyperbolic groups admit Anosov embeddings into higher-rank Lie groups.
Study proves hyperbolic groups have specific subgroup properties.
problem Characterizing subgroups of word hyperbolic groups.
method Analyzes Anosov representations into .
result Affirmative answer to Sambarino's question for Borel Anosov representations.
New metrics for Anosov representations defined from Thurston's asymmetric metrics.
problem Defining metrics for Anosov representations.
method Generalizing Thurston's asymmetric metric to Anosov representations.
result Provides a (possibly asymmetric) Finsler distance in some cases.
Cataclysm deformations study Anosov representations and their convergence.
problem Understanding convergence of Anosov representations under deformation.
method Cataclysm deformation of Anosov representations using twisted transverse cocycles.
result Uniform convergence of cataclysm deformations on compact sets.
Anosov deformations created for surfaces with specific properties.
problem Creating proper slices in character varieties for specific surface groups.
method Constructing proper slices in character varieties for surface groups into SL(3,R).
result Representations are Borel Anosov.
Cataclysm deformations study Anosov representations, leading to new formulas and non-open sets.
problem Understanding Anosov representations and their deformations.
method Cataclysm deformations based on twisted transverse cocycles.
result Uniform convergence of cataclysm deformations on compact sets.
Proves restrictions on projective Anosov representations of hyperbolic groups.
problem Restrictions on projective Anosov representations of hyperbolic groups.
method Word hyperbolic groups and Gromov boundary analysis.
result Word hyperbolic groups with certain properties cannot admit projective Anosov representations.
Anosov groups study matrix coefficients and orbit counting in symmetric spaces.
problem Anosov groups and their matrix coefficients in symmetric spaces.
method Asymptotic analysis of matrix coefficients and higher rank measures.
result Asymptotic behavior of matrix coefficients and orbit counting results.
Study of Anosov representations with Lipschitz limit set and applications to rigidity.
problem Characterizing Anosov representations with specific limit set properties.
method Introducing an unstable Jacobian and analyzing its orbit growth rate.
result Many higher rank representations belong to the studied class.
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.
New examples of embeddings defy Anosov representation limits.
problem Examples of robust quasi-isometric embeddings not approximated by Anosov representations.
method Exhibited non-locally rigid, Zariski dense embeddings in .
result Higher rank Anosov representation theorems fail for .
The paper proves identities for hyperconvex Anosov representations and their applications to Cantor sets.
problem Establishing identities for hyperconvex Anosov representations.
method Analyzing holomorphic families of Cantor non-conformal repellers and studying series identities.
result The series is absolutely summable if and only if the Hausdorff dimension of the Cantor set is less than 1.
We study the limit set of discrete subgroups arising from Anosov representations. Specially we study the limit set of discrete groups arising from strictly convex real projective structures and Anosov representations from a finitely generated word hyperbolic group into a semisimple Lie group.
New insights into Anosov representations of hyperbolic groups.
problem Understanding Anosov representations of relatively hyperbolic groups.
method Proving representations can be interpreted as restricted Anosov representations over flow spaces and showing stability under deformations.
result Representations of certain types are divergent, extended geometrically finite and stable under small deformations.