New infinite discrete group without finite quotients found.
problem Finding discrete groups without finite quotients.
method Constructing an infinite discrete subgroup of .
result Infinite discrete subgroup with no finite non-trivial quotients.
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48 results for “infinite discrete groups”
Homological stability proved for discrete surface diffeomorphisms.
problem Homological stability of surface diffeomorphisms made discrete.
method Infinite loop space construction and characteristic class analysis.
result Stable homology of discrete surface diffeomorphisms is the same as a related infinite loop space.
The paper proves that certain spaces have injective balls of any radius.
problem The injectivity radius of certain geometric spaces is infinite.
method Analyzes higher rank simple and semisimple Lie groups with specific properties.
result The locally symmetric spaces have injective balls of any radius.
Study of vector bundles over classifying spaces for infinite discrete groups.
problem Understanding vector bundles over classifying spaces for infinite discrete groups.
method Homotopy theoretical framework for infinite discrete groups, relating to Novikov conjecture.
result Established a connection between representation spaces and vector bundles over classifying spaces.
We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dens…
The study proves limitations on isospectral hyperbolic surfaces with discrete length spectra.
problem Characterizing isospectral hyperbolic surfaces with discrete length spectra.
method Utilizing Sunada's method and topological self-duplicating ends, the study explores isospectral families and their cardinality.
result Finite groups can be realized as full isometry groups of hyperbolic structures with discrete spectrum on surfaces with self-duplicating ends.
New pseudomodular groups constructed from jigsaw construction.
problem Existence and properties of pseudomodular groups.
method Jigsaw construction of groups.
result Infinitely many simplest jigsaw groups are not pseudomodular.
The paper characterizes geometric infiniteness for convergence group actions using orbit uniform metrics.
problem Characterizing geometric infiniteness for convergence group actions.
method Introducing orbit uniform metrics and proving properties of discrete orbits.
result Characterization of geometric infiniteness in terms of uncountability of non-conical limit points and existence of escaping sequences.
Improved homological dimension for certain subgroups in Lie groups.
problem Determining homological dimensions of discrete subgroups in Lie groups.
method Using recent results and properties of injectivity radius, the homological dimension gap is calculated.
result Infinite volume torsion-free subgroups of higher rank Lie groups have a homological dimension gap of at least 1/8 of the real rank.
Smooth resolutions found for quotient of R^2 by infinite discrete groups.
problem Symplectic resolutions of quotient spaces by infinite discrete subgroups.
method Constructing smooth symplectic resolutions for R^2 under infinite discrete subgroups of GL_2(R).
result Minimal resolutions of Du Val singular varieties are symplectic resolutions of R^2/G.
The paper shows commensurators of certain subgroups are discrete.
problem Understanding commensurators of specific subgroups in Lie groups.
method Analyzing commensurators of thin normal subgroups with abelian quotients.
result The commensurator of certain subgroups is discrete.
We extend a work of Bartsch, Clapp and Puppe on the Mountain pass theorems. We consider functionals invariant with respect to infinite discrete groups satisfying a maximality condition on the finite subgroups.
We survey some results and questions about free actions of infinite groups on products of spheres and euclidean spaces, and give some new co-compact examples.
The study finds discrete subgroups with full limit sets in higher rank Lie groups.
problem Finding discrete subgroups with full limit sets in higher rank Lie groups.
method Analyzing real semi-simple Lie groups of higher rank and providing criteria for discrete subgroups of .
result Existence of discrete subgroups with full limit sets in higher rank Lie groups.
New insights into ends of quotient spaces and graphs.
problem Understanding the ends of quotient spaces and graphs.
method Analyzing infinite volume ends of quotient spaces and graphs.
result Quotient spaces and graphs have exactly one infinite volume end under certain conditions.
Research covers geometry, analysis, and integration on infinite-dimensional spaces.
problem Exploring geometric and analytical structures in infinite-dimensional settings.
method Analyzes numerical schemes, Lie groups, connections, and integration theory.
result Developed new methods for integration and analysis on infinite-dimensional manifolds.
We describe a family of 4-dimensional hyperbolic orbifolds, constructed by deforming an infinite volume orbifold obtained from the ideal, hyperbolic 24-cell by removing two walls. This family provides an infinite number of infinitesimally rigid, infinite covolume, geometrically finite discrete subgroups of the isometry…
Study infinite subgroups of higher rank Lie groups, focusing on Anosov subgroups.
problem Understanding properties of Anosov subgroups in higher rank semisimple Lie groups.
method Characterize Anosov subgroups through geometric, coarse geometric, and dynamical viewpoints.
result New equivalent characterizations of Anosov subgroups, capturing rank one behavior.
The paper constructs surfaces with infinite-genus Veech groups from finite subgroups of GL(2, R).
problem Constructing surfaces with specific Veech groups from given subgroups.
method PSV construction and modifications to produce tame translation surfaces.
result Ends of constructed surfaces can be decomposed into a group's ends and a dense subset.
Study shows singularity of stationary measure on Furstenberg boundary for certain random walks.
problem Singularity of stationary measure on Furstenberg boundary for random walks.
method Analysis of random walks on semisimple Lie groups with specific properties.
result Stationary measure is singular to Lebesgue measure in certain cases.
Extends Nielsen realization to infinite-type surfaces, classifying torsion elements and topological groups.
problem Realizing finite subgroups of mapping class groups on infinite-type surfaces.
method Extending Kerckhoff's result to infinite-type surfaces, using hyperbolic metrics and topological group properties.
result Compact subgroups of mapping class groups are finite, and locally compact subgroups are discrete.
The paper studies symplectic surface bundles and their characteristic classes.
problem Understanding characteristic classes of symplectic surface bundles.
method Homological stability of symplectomorphisms and extended Hamiltonians, isomorphism construction, infinite loop spaces.
result Homotopy theoretic proof of the Kotschick-Morita theorem.
The paper finds free semigroups in dense subgroups of Lie groups with critical exponents arbitrarily close to the subgroup's.
problem Finding free semigroups with critical exponents arbitrarily close to a subgroup's in dense subgroups of Lie groups.
method Analyzing Zariski dense discrete subgroups of Lie groups, showing the existence of free semigroups with critical exponents arbitrarily close to the subgroup's.
result The existence of free semigroups with critical exponents arbitrarily close to the subgroup's in dense subgroups of Lie groups.
Study thin hyperbolic reflection groups and their properties.
problem Characterize and enumerate thin hyperbolic reflection groups.
method Analyze Zariski dense subgroups of hyperbolic isometries, apply Vinberg algorithm.
result All thin hyperbolic reflection groups are enumerable.
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed. Special attention is paid to the case of mappings between topological vector spaces ov…
Study large-scale geometry of graph braid groups via cubical structures.
problem Classify and understand the quasi-isometry of graph braid groups.
method Exploit cubical structures to relate hyperbolicity, undistorted subgroups, and group decompositions.
result Complete classification of graph braid groups quasi-isometric to free groups.
This paper reconstructs Lie groupoids from their bisections and applies it to prequantisation.
problem Reconstructing Lie groupoids from their bisections and applying it to prequantisation.
method Investigates the relation of bisections to Lie groupoids and constructs Lie groupoids from bisection Lie groups using recent progress in the infinite-dimensional Frobenius theorem.
result Characterizes an integrability constraint of closed Lie subalgebras to closed Lie subgroups in terms of modified discreteness conditions on periods.
By using Thurston's bending construction we obtain a sequence of faithful discrete representations ρ_n of the fundamental group of a closed hyperbolic 3-manifold fibering over the circle into the isometry group Iso H^4 of the hyperbolic space H^4. The algebraic limit of ρ_n contains a finitely generated subgroup F whos…
We study discrete, cocompact, isometric actions of groups on Hadamard spaces, and the induced actions on ideal boundaries. For a class of groups generalizing fundamental groups of three-dimensional graph manifolds, we find a set of invariants for the action which determine the boundary action up to equivariant homeomor…
Assembly maps study topological cyclic homology of group algebras at primes.
problem Study topological cyclic homology of group algebras at primes.
method Use assembly maps to analyze for various groups.
result Proves various properties of assembly maps for different groups.
Infinite volume requires no atoms at the bottom of the spectrum for certain groups.
problem Determining conditions for infinite volume in certain algebraic groups.
method Analyzing the spectral properties of Laplace operators on symmetric spaces.
result The bottom of the -spectrum being an atom is necessary and sufficient for finite volume.
We prove that group homology of the diffeomorphism group of as a discrete group is independent of in a range, provided that . This answers the high dimensional version of a question posed by Morita about surface diffeomorphism groups made discrete. The stable homology is isomorphic to the…
New findings on infinite subgroups in negatively curved spaces.
problem Characterizing infinite discrete isometry subgroups in negatively pinched Hadamard manifolds.
method Generalization of Bonahon's characterization to negatively pinched Hadamard manifolds.
result Every geometrically infinite isometry subgroup has a continuum of nonconical limit points.
Arithmetic topology connects surface and -adic field studies, enabling new insights into Galois groups.
problem Understanding the relationship between surfaces and -adic fields through arithmetic topology.
method Uniform approach using pro- groups, graph of groups, and discrete splittings.
result Infinite order arithmetic Dehn twists in Galois groups, connecting to classical Dehn twists on surfaces.
Study shows almost minimizing rectifiable chains in Hilbert space have regular points dense in their support.
problem Understanding the regularity of almost minimizing rectifiable chains in infinite dimensional spaces.
method Adapted Reifenberg's epiperimetric inequality and computations by Preiss to infinite dimensional space.
result The set of regular points is dense in the support of almost mass minimizing rectifiable chains.
Generalizing a classical theorem of Carlson and Toledo, we prove that any Zariski dense isometric action of a Kähler group on the real hyperbolic space of dimension at least 3 factors through a homomorphism onto a cocompact discrete subgroup of PSL(2,R). We also study actions of Kähler groups on infinite dimensional re…
The paper extends geometric finiteness to discrete subgroups of negatively pinched Hadamard manifolds.
problem Characterizing geometrically infinite discrete subgroups of negatively pinched Hadamard manifolds.
method Generalizing Bonahon's characterization and proving a theorem of Bishop's extension.
result Every discrete geometrically infinite isometry subgroup has a set of nonconical limit points of cardinality continuum.
Extends Floquet-Bloch theory to nilpotent groups for geometric applications.
problem Asymptotic problems on nilpotent covers of negatively curved manifolds.
method Generalized Floquet-Bloch theory using Malcev completions.
result Branching formula relating finite and infinite-dimensional representations.
We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras integrates to a corresponding Lie group extension of by , where is a connected, simply connected Lie group and is a quotient of its Lie algebra by some discrete subgroup. When is non-simply connected…
The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin braid groups, a class of virtually poly-surface groups and virtually solvable lin…
New groups discovered with unique properties in a specific space.
problem Finding new discrete subgroups with special properties in a mathematical space.
method Proved by showing groups play ping-pong on cones, related to crooked surfaces.
result Infinite family of discrete subgroups with remarkable properties in .
Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that the boundary of X has no cut points and that one can detect splittings of over two-ended groups and recover its JSJ decomposition from the boundary. We show that any discrete action of a group G on a CAT(0) space X satis…
Study complex reflections in infinite Coxeter tetrahedron moduli space.
problem Characterize representations of Coxeter group in complex hyperbolic space.
method Type-preserving representations of Coxeter group to , parameterized by .
result Discrete and faithful representations for . First nontrivial moduli space in complex hyperbolic space.
Proves finite measure implies product structure for certain discrete subgroups.
problem Classifying discrete subgroups with finite Bowen-Margulis-Sullivan measure.
method Product structure of leafwise measures and high entropy method.
result Proves virtually a product structure for certain subgroups.
Totally non congruence Veech groups found in translation surfaces.
problem Understanding Veech groups in translation surfaces.
method Analyzing origamis and their Veech groups in various strata of translation surfaces.
result Infinitely many origamis have totally non congruence Veech groups.
This paper classifies commutativity spaces for 3-manifold groups.
problem Classifying commutativity spaces for geometric 3-manifold groups.
method Using geometric realization of order complexes of cosets of abelian subgroups.
result For closed orientable geometric 3-manifolds, the commutativity space is homotopy equivalent to a wedge of circles.
We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN…
New non-rigid discrete groups found in hyperbolic spaces.
problem Uniqueness of conformal or spherical CR structures on spheres.
method Nilpotent Sierpiński carpet and stretching to construct non-rigid groups.
result Discrete hyperbolic groups can have non-rigid deformations.