Finite group action on a surface yields a special homology subspace.
problem Finite group action on a surface.
method Invariant Lagrangian subspace in homology.
result Existence of a G-invariant Lagrangian subspace in H1(S).
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48 results for “action subspace”
We study isometric cohomogeneity one actions on the (n+1)-dimensional Minkowski space up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on the Minkowski space whose orbit spaces are non-Hausdorff. We show that there exist isometric cohomogeneity one actions on the Minkowski space which ar…
Roweisposes, Including Eigenposes, Supervised Eigenposes, and Fisherposes, for 3D Action Recognitioncs.CV
Paper proposes Roweisposes for 3D action recognition using generalized eigenvalue problem.
problem Need for basic methods in 3D action recognition.
method Roweisposes uses Roweis discriminant analysis for generalized subspace learning.
result Roweisposes is effective for 3D action recognition.
This paper classifies Hamiltonian actions by symplectic groupoids using Delzant subspaces.
problem Classifying Hamiltonian actions by regular proper symplectic groupoids.
method Using Delzant subspaces and cohomology groups to classify actions.
result Classifies faithful multiplicity-free Hamiltonian actions in terms of Delzant subspaces.
Representation of human actions as a sequence of human body movements or action attributes enables the development of models for human activity recognition and summarization. We present an extension of the low-rank representation (LRR) model, termed the clustering-aware structure-constrained low-rank representation (CS…
Study mapping class group action on de Rham quasimorphisms, finding no fixed points.
problem Action of mapping class group on de Rham quasimorphisms.
method Examined the action of mapping class group on de Rham classes in bounded cohomology of a hyperbolic surface.
result No fixed points in the action of mapping class group on de Rham quasimorphisms.
We study the geometry of an important class of generic curves in the Grassmannian manifolds of -dimensional subspaces and Lagrangian subspaces of under the action of the linear and linear symplectic group.
Extends Kähler metrics theory to symplectic manifolds with toric actions.
problem Extending invariant Kähler metrics theory to symplectic manifolds with toric actions.
method Using Delzant subspaces and Lagrangian fibrations, establishing a correspondence between metrics and connections.
result Characterizes extremal invariant Kähler metrics as those with scalar curvature on base integral affine manifold.
I construct an algebraic model for a typical fiber on a 1+1 dimensional spacetime. The vector space comprising the fiber is composed of elements formed from the direct product of two copies of an element x in the D2=C2xC2 finite group algebra over the real numbers. The fiber contains subspaces whose elements are associ…
TOFU-POV tackles partially observed linear bandits, achieving sublinear regret with low-dimensional action vectors.
problem Stochastic linear bandits with partially observed actions in settings like recommendation and healthcare.
method TOFU-POV estimates latent action subspace, imputes missing actions, and runs OFUL in low-dimensional coordinates.
result TOFU-POV achieves regret scaling with intrinsic subspace dimension, improving upon natural baselines.
In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such group-invariant subspaces are also referred to as su…
The paper constructs submanifolds with corners in Delzant polytopes from affine subspaces.
problem Understanding submanifolds with corners in Delzant polytopes.
method Constructing submanifolds with corners in Delzant polytopes from affine subspaces.
result Conditions for submanifolds with corners are equivalent to those for torus-equivariantly embedded toric manifolds.
Defines action on knot spaces using cacti and cubes.
problem Understanding the space of framed long knots.
method Defines an action of cacti operad on the Taylor tower of framed long knots.
result Improves previous work on Vassiliev invariants.
Classifies actions on complex space forms with Lagrangian orbits.
problem Classifying actions on complex space forms with Lagrangian orbits.
method Classifies holomorphic isometric actions on complex space forms.
result Only examples are Lagrangian affine subspace foliations of complex Euclidean spaces and Lagrangian horocycle foliations of complex hyperbolic spaces.
Church-Ellenberg-Farb used the language of FI-modules to prove that the cohomology of certain sequences of hyperplane arrangements with S_n-actions satisfies representation stability. Here we lift their results to the level of the arrangements themselves, and define when a collection of arrangements is "finitely genera…
Optimal smooth subspaces approximate large data sets efficiently.
problem Approximating large data sets with invariant subspaces.
method Smooth functions under lattice translations or crystallographic groups, with optimal selection of Paley-Wiener space.
result Optimal lattice selection enhances approximation efficiency.
POSA optimizes policy gradients by reducing variance with RB and CV.
problem High variance in policy gradient estimators for high-dimensional control tasks.
method POSA uses ASDG estimator combining RB and CV, learning action space factorization.
result POSA improves performance on high-dimensional control tasks.
The paper explores how the cohomology of certain space arrangements stabilizes as the number of subspaces increases.
problem Stability of cohomology groups of complements of linear subspace arrangements.
method Representation stability in the context of cohomology groups, focusing on arrangements invariant under permutation of coordinates.
result Bounds on stabilization and alternative proof for the stabilization of cohomology groups.
For a Veech surface (x,ω), we characterize subspaces of X^n, invariant under the diagonal action of the affine group of X. We prove that non-arithmetic Veech surfaces have only finitely many invariant subspaces of very particular shape (in any dimension). Among other consequences we find copies of (X,ω) embedded in the…
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we explicitly determine the dependance of coefficients of generalized symmetries fro…
We provide abelianizations of differentiable actions of finite groups on smooth real manifolds. De Concini-Procesi wonderful models for (local) subspace arrangements and a careful analysis of linear actions on real vector spaces are at the core of our construction. In fact, we show that our abelianizations have stabili…
Spaces of Knotsmath.GT
We consider the space of all smooth knots in the 3-sphere isotopic to a given knot, with the aim of finding a small subspace onto which this large space deformation retracts. For torus knots and many hyperbolic knots we show the subspace can be taken to be the orbit of a single maximally symmetric placement of the knot…
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.
An operad for splicingmath.GT
A new topological operad is introduced, called the splicing operad. This operad acts on a broad class of spaces of self-embeddings N --> N where N is a manifold. The action of this operad on EC(j,M) (self embeddings R^j x M --> R^j x M with support in I^j x M) is an extension of the action of the operad of (j+1)-cubes …
A Braid Boxmath.HO
Interactive art piece shows braid groups and plane motions.
problem Understanding braid groups and their actions.
method Interactive art piece illustrating two braid group definitions and their action on free group.
result Demonstrates all plane motions in a single subspace.
The study finds Lie algebra formulae and classifies polar actions on a hyperbolic plane.
problem Finding Lie algebra formulae and classifying actions on hyperbolic planes.
method Using octonions and triality, explicit Lie brackets were found for Lie algebras of isometry groups.
result Explicit formulae for Lie brackets of and Lie algebras.
We develop a method of extending actions of compact transformation groups which is then applied to the problem of preservation of equivariant extensor property by passing to a subspace of given orbit types.
CAT(0) spaces can split into products if their boundary has certain properties.
problem Detecting product splittings in CAT(0) spaces.
method Analyzing the boundary properties of CAT(0) spaces and their group actions.
result Conditions for a CAT(0) space to contain a quasi-dense, closed convex subspace that splits as a product.
New submanifolds found in toric manifolds with specific actions.
problem Understanding submanifolds in toric manifolds with complex subtorus actions.
method Analyzing the closure of a complex subtorus in a toric manifold and its Hamiltonian action.
result The image of the moment map for the Hamiltonian subtorus action coincides with the image of the Delzant polytope.
To each ribbon graph we assign a so-called L-space, which is a Lagrangian subspace in an even-dimensional vector space with the standard symplectic form. This invariant generalizes the notion of the intersection matrix of a chord diagram. Moreover, the actions of Morse perestroikas (or taking a partial dual) and Vassil…
The paper studies control data and equivariant properties of stratified spaces.
problem Equivariant properties of stratified spaces with group actions.
method Equivariant submersion theorem and control data construction.
result Inclusion of -stratified subspaces is a -equivariant cofibration.
We prove that the kernels of the restrictions of symplectic Dirac or symplectic Dirac-Dolbeault operators on natural subspaces of polynomial valued spinor fields are finite dimensional on a compact symplectic manifold. We compute those kernels for the complex projective spaces. We construct injections of subgroups of t…
A new tensor-based method improves multi-dimensional data classification accuracy.
problem Efficient representation and classification of multi-dimensional data from multiple sensors.
method n-mode generalized difference subspace (n-mode GDS) for tensor data, with improved metric based on geodesic distance.
result The proposed method outperforms existing methods in gesture and action recognition.
Quantum CNNs can be efficiently simulated classically on simple datasets.
problem Quantum CNNs' success on simple datasets is due to low-bodyness measurements.
method Classical simulation using Pauli shadows on low-bodyness subspace.
result Quantum CNNs' action on low-bodyness subspace can be efficiently simulated classically.
Classifies cobounded hyperbolic actions of metabelian groups.
problem Classify cobounded hyperbolic actions of metabelian groups.
method Builds connections between hyperbolic geometry and commutative algebra to classify actions.
result Classifies cobounded hyperbolic actions of many abelian-by-cyclic groups.
Minimal orbits of semi-simple Lie groups are studied and related to invariant subspaces.
problem Characterizing minimal orbits of semi-simple Lie groups.
method Analyzing projective orbits induced by representations of semi-simple Lie groups and relating them to invariant subspaces of the underlying modules.
result Minimal orbits of semi-simple Lie groups are in bijection with minimal orbits of compact subgroups on invariant subspaces.
New result on group actions in CAT(0) spaces with vanishing escape rate.
problem Understanding group actions with vanishing escape rate on CAT(0) spaces.
method Equivariant -harmonic map proof.
result Existence of a flat subspace invariant under the action of .
The paper studies cohomogeneity one actions on pseudo-Euclidean space and identifies unique orbit structures.
problem Characterizing cohomogeneity one actions on pseudo-Euclidean spaces.
method Analyzing isometric linear actions of subgroups of the isometry group of .
result Identified unique orbit structures of cohomogeneity one actions on .
The Flag Median and FlagIRLSstat.ML
New subspace prototype flag median improves clustering on noisy data.
problem Finding robust prototypes for datasets of images and videos.
method Proposes flag median and introduces FlagIRLS algorithm for its calculation.
result Flag median is robust to outliers and improves cluster purity.
The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.
The paper studies ergodicity of flows on subspaces, generalizing earlier work.
problem Ergodicity of flows on subspaces of higher rank groups.
method Analyzes one-parameter diagonalizable subgroups of connected semisimple groups acting on homogeneous spaces.
result Obtains an ergodicity criterion similar to Hopf-Tsuji-Sullivan for general Anosov subgroups.
Algorithm reduces high-dimensional SLB regret by exploiting hidden low-rank structure.
problem High-dimensional stochastic linear bandits with hidden low-rank structure.
method Projective Stochastic Linear Bandit (PSLB) using PCA projection.
result PSLB achieves tighter regret bound and faster convergence.
In this paper, we introduce the notion of maximal actions of compact tori on smooth manifolds and study compact connected complex manifolds equipped with maximal actions of compact tori. We give a complete classification of such manifolds, in terms of combinatorial objects, which are triples of n…
Non-abelian GKM Theorymath.DG
We describe a generalization of GKM theory for actions of arbitrary compact connected Lie groups. To an action satisfying the non-abelian GKM conditions we attach a graph encoding the structure of the non-abelian 1-skeleton, i.e., the subspace of points with isotopy rank at most one less than the rank of the acting gro…
Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the space R := Hom(G, Isom(M)) with the compact open topology. Sample theorems: 1. The…
The paper proves a Calabi-Yau structure on complexifications of rank two symmetric spaces.
problem Existence of Calabi-Yau structures on complexifications of symmetric spaces.
method Using orbit geometry and shape operators, the authors prove the existence of a Calabi-Yau structure.
result A Calabi-Yau structure exists on the complexification of rank two symmetric spaces.
For dimensions n greater than or equal to 3, we show that the space of metrics of positive scalar curvature on the n-sphere is homotopy equivalent to a subspace which takes the form of a H-space with a homotopy commutative, homotopy associative product operation. This product operation is based on the connected sum con…
Constructs equivariant embeddings of Hermitian symmetric spaces into tangent spaces.
problem Embedding Hermitian symmetric spaces into their tangent spaces.
method Using polarity of the K-action to construct equivariant embeddings.
result Characterizes holomorphic/symplectic embeddings and realizes submanifolds.