One-relator groups with torsion are shown to be coherent.
problem One-relator groups with torsion.
method Demonstrated coherence by showing every finitely generated subgroup is finitely presented.
result One-relator groups with torsion are coherent.
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48 results for “coherent groups”
Extends coherence results to one-relator products of locally indicable groups.
problem Coherence in one-relator products of locally indicable groups.
method Developed new methods to extend results of Helfer, Wise, Louder, Wilton, and Brodsky.
result New proof of a theorem by Brodsky.
A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a map between two finite 2-complexes which is introduced here. In the groups to whic…
Proves Tits alternative for specific PD(3) groups.
problem Tits alternative for groups.
method Proving Tits alternative for almost coherent groups.
result Almost coherent groups contain rank 2 free groups.
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space…
The study examines Kähler structures on coadjoint orbits of Lie groups using coherent and squeezed states.
problem Does the coadjoint orbits of Lie groups support a Kähler structure?
method Examined three Lie groups: Weyl-Heisenberg, SU(2), and SU(1,1). Used coherent and squeezed states to explore Kähler structures.
result Coherent states provide Kähler embeddings, while squeezed states only symplectic embeddings.
Develops equivariant Chern characters for coherent sheaves with group actions.
problem Computing Chern characters for coherent sheaves on manifolds with group actions.
method Introduces equivariant Chern characters and proves Riemann-Roch-Grothendieck theorem in Bott-Chern cohomology.
result Establishes a Riemann-Roch-Grothendieck theorem for coherent sheaves with finite group actions.
Uniform negative immersions prove coherence of one-relator groups.
problem Proving coherence of one-relator groups.
method Using uniform negative immersions and linear-programming techniques.
result One-relator groups with uniform negative immersions are coherent.
Non-coherence proven for certain groups with specific mapping tori.
problem Proving non-coherence for groups with specific mapping tori.
method Analyzing the structure of groups as extensions and properties of mapping tori.
result Groups with certain mapping tori are not coherent.
Financial markets have been extensively studied as highly complex evolving systems. In this paper, we quantify financial price fluctuations through a coupled dynamical system composed of phase oscillators. We find a Financial Coherence and Incoherence (FCI) coexistence collective behavior emerges as the system evolves …
Study shows exotic Dehn twists on certain 3-sphere fillings.
problem Extending group actions from boundaries to interiors of 4-manifolds.
method Analyzing Dehn twists on Seifert homology spheres and their fillings.
result Dehn twists on certain fillings are infinite order exotic.
The weak regular coherence is a coarse property of a finitely generated group . It was introduced by G. Carlsson and this author to play the role of a weakening of Waldhausen's regular coherence as part of computation of the integral K-theoretic assembly map. A new class of metric spaces (sFDC) was introduced recent…
This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse -structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends to the category of coherent sheaves equivariant under an action of an algebraic …
A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.
Coherent manifoldsmath-ph
Defines coherent manifolds and their quantum applications.
problem Understanding quantum spaces and coherent states.
method Generalizes quantum field theory and Schrödinger equation solutions.
result Solves Schrödinger equation on coherent manifolds.
New non-kinetic actions on four-manifolds discovered.
problem Finding non-kinetic smooth homotopy coherent actions on four-manifolds.
method Restricting a nontrivial action on a surface and constructing extensions.
result First example of a non-kinetic smooth homotopy coherent action of order two on a four-manifold.
The paper finds incommensurable lattices in complex models of Baumslag-Solitar groups.
problem Locally finite 2-complexes and their automorphism groups contain incommensurable lattices.
method Constructing lattices in combinatorial models of Baumslag-Solitar groups and analyzing their properties.
result The constructed lattices are incommensurable and have specific properties like isomorphic Cayley graphs.
Let be an algebraic curve of genus . A coherent system on consists of a pair , where is an algebraic vector bundle over of rank and degree and is a subspace of dimension of the space of sections of . The stability of the coherent system depends on a parameter . We study t…
It is shown that the heat operator in the Hall coherent state transform for a compact Lie group is related with a Hermitian connection associated to a natural one-parameter family of complex structures on . The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizati…
Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for linear Hamiltonians in the generators of the groups first order differential equati…
The intimate relationship between coherent states and geodesics is pointed out. For homogenous manifolds on which the exponential from the Lie algebra to the Lie group equals the geodesic exponential, and in particular for symmetric spaces, it is proved that the cut locus of the point is equal to the set of coheren…
The coherent state representation of the Jacobi group is indexed with two parameters, , describing the part coming from the Heisenberg group, and , characterizing the positive discrete series representation of . The Ricci form, the scalar curvature and the geodesics of th…
Quantizes Toda systems using geometric methods.
problem Quantizing Toda systems with geometric quantization.
method Geometric quantization of Toda systems as a coadjoint orbit of a group of matrices.
result Found unitary and non-unitary finite dimensional quantum Hilbert spaces.
We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which covers the case that G acts freely. Our extension of these results involves a generalization of the notion of sectional curvat…
Constructs 2-representations and 2-vector bundles for Lie 2-groups.
problem No strict model for string 2-group, so coherent model is constructed.
method Builds category of 2-representations and equivariant 2-vector bundles.
result Explicit formulas for 2-representations and 2-vector bundles.
Coherent structure coloring: identification of coherent structures from sparse data using graph theoryphysics.flu-dyn
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…
New method groups genetic data into coherent topics for disease insights.
problem Analyzing large, multi-dimensional genetic data sets.
method Conditional Hierarchical Bayesian Tucker Decomposition for genetic data analysis.
result Our models are more coherent than baseline models.
Dehn twists on K3-type 4-manifolds are not homotopy coherently Nielsen realizable.
problem Homotopy coherent Nielsen realization problem for Dehn twists on 4-manifolds
method Using family Seiberg-Witten theory
result Failure of the classical Nielsen realization problem in K3-type 4-manifolds
New Thurston norm defined for a specific type of groups using -invariants.
problem Measuring splitting complexity of integral characters in coherent right-angled Artin groups.
method Defining splitting complexity via -Euler characteristic and using Friedl--Lück's -polytope.
result A Thurston-type semi-norm defined for measuring splitting complexity of integral characters.
Polynomial representations found in surface braid and mapping class groups.
problem Homological representations of surface braid and mapping class groups.
method Study of homological representation functors and short exact sequences.
result Many homological representation functors are polynomial.
Enhances neural forecasting for hierarchically organized time series data.
problem Probabilistic coherent forecasting of time series data across different levels of aggregation.
method Proposes a coherent multivariate mixture output for neural forecasting architectures, optimizing with a composite likelihood objective.
result 13.2% average accuracy improvements on most datasets compared to state-of-the-art baselines.
The paper studies geometric quantization and coherent state transforms on Lie groups.
problem Quantization of cotangent bundles of compact Lie groups with new invariant structures.
method Analytic continuation of Hamiltonian flows on -invariant Kähler structures.
result Partial coherent state transforms and new Kähler structures on .
New description of L-space knots leads to non-left-orderable surgeries.
problem Characterizing and understanding L-space knots.
method Analyzing coherent reduced -diagrams to describe L-space knots and proving non-left-orderable fundamental groups.
result Any L-space obtained by Dehn surgery on a -knot in has a non-left-orderable fundamental group.
Smooth actions of infinite groups linked to homotopy theory.
problem Connecting infinite-dimensional smooth groups to homotopy theory.
method Two computations: diffeological homotopy groups and localization of a strict category.
result Natural constructions yield homotopically coherent group actions of G.
The study of topological groups with compact open subgroups and their geometric properties.
problem Characterizing and understanding topological groups with compact open subgroups.
method Geometric techniques, discrete actions on complexes, quasi-isometry invariance, and hyperbolic fine graphs.
result Generalizations of discrete group results to topological groups with compact open subgroups.
Survey on algebraic fibers of group extensions and their finiteness properties.
problem Existence and finiteness of algebraic fibers in group extensions.
method Analysis of abstract and pro- groups.
result Finiteness properties of algebraic fibers in group extensions.
The study shows higher incoherence in automorphism groups of free groups.
problem Understanding the finiteness properties of automorphism groups of free groups.
method Analyzing extensions of a finite-index subgroup of Aut(F_2) and using fiber maps.
result Upper bounds on the coherence of automorphism groups of free groups.
Conference compiles problems on foliations and diffeomorphisms.
problem Challenges in foliations and diffeomorphism groups.
method Compilation of problems from conference participants.
result Compilation of 20+ problems on foliations and diffeomorphisms.
Clustering groups similar data points into clusters.
problem Grouping similar data points into coherent clusters.
method Different clustering methods based on similarity and data representations.
result Various clustering methods exist.
The paper constructs a model for the string 2-group using the free loop group.
problem The string 2-group lacks a strict Lie-2-group model with circle group action.
method Using the free loop group (or ), the paper constructs a coherent model for the string 2-group with explicit formulas.
result There are obstructions for constructing a strict model for the string 2-group using the free loop group.
The paper constructs coronas for combable spaces under specific conditions.
problem Constructing boundaries for combable spaces.
method Introducing properness, coherence, and expandingness for combings; constructing coronas using Rips complexes.
result Bijectivity of transgression maps, injectivity of the coarse assembly map, and surjectivity of the coarse co-assembly map for groups.
Let be a diagonal linear operator on $\C^n$, with all eigenvalues satisfying , and $M = (\C^n\backslash 0)/<A>$ the corresponding Hopf manifold. We show that any stable holomorphic bundle on can be lifted to a -equivariant coherent sheaf on $\C^n$, where $G=(\C^*)^l$ is a Lie group acting on $\C^n…
HierarchicalForecast provides a Python framework for coherent hierarchical forecasting.
problem Ensuring forecasts at disaggregate levels add up to aggregate forecasts.
method Preprocessed datasets, evaluation metrics, and statistical baseline models.
result Python-based reference framework for statistical and ML forecasting.
CoRe method improves time series forecasting coherency without strict constraints.
problem Noisy hierarchical time series data that doesn't perfectly adhere to aggregation constraints.
method Coherency Regularization using neural networks.
result Improved forecast accuracy and coherence, especially in noisy data scenarios.
In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …
Study properties of group rings of three-manifold groups.
problem Properties of group rings of three-manifold groups.
method By piecing together known facts about three-manifold groups, the paper establishes two properties of the group ring .
result If has rational cohomological dimension two, then is coherent. If is torsion-free, then satisfies the Strong Atiyah Conjecture over and satisfies Kaplansky's Zero Divisor Conjecture.
Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.
problem Identifying and visualizing coherence among multiple time series.
method Fast spectral similarity based on cosine similarity metrics of Fourier-transformed signals and sparse time-frequency wavelet coherence.
result Scalable real-time system for low-latency inference and monitoring of inter-signal relationships.
A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This …