arXiv research

The paper connects knot representations and spherical quandle colorings.

Study local features of decorated representation spaces for spherical surfaces.

Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\infty/K_\infty = \varinjlim G_n/K_n$. We use the representation t…

Defines spherical type surfaces via support function and classifies them.

In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indi…

In this paper, new representations of a Bertrand curve pair in three dimensional Lie groups with bi-invariant metric are given. Besides, the spherical indicatrices of a Bertrand curve pair are obtain and the relations between the spherical indicatrices and new representations of Bertrand curve pair are shown.

In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms …

We classify hyperbolic monopoles with continuous symmetries and construct new examples.

Paper introduces spherical knot mosaics for knot and link invariants.

In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representatio…

A spherical topological manifold of dimension n-1 forms a prototile on its cover, the (n-1)-sphere. The tiling is generated by the fixpoint-free action of the group of deck transformations. By a general theorem, this group is isomorphic to the first homotopy group. Multiplicity and selection rules appear in the form of…

Study shows negatively curved manifolds' spherical volume equals minimal surface area.

Study $Θ$-invariants for spherical 3-manifolds via $\mathbb{Z}π$-homology equivalences.

Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.

We prove that M. Kramer's classification of list of spherical pairs coincides with that for weakly symmetric spaces by examining the linear isotropy representation of the corresponding homogeneous space associated to each pair.

A new spherical Sliced-Wasserstein distance for data on spheres.

We consider the discrete representations of 3-manifold groups into $PU(2,1)$ that appear in the Falbel-Koseleff-Rouillier census, such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations have conjugate images, even though they represent different 3-manifold groups. Th…

Study spherical Fourier transform on hypergeometric type harmonic manifolds.

We obtain a branched spherical CR structure on the complement of the figure eight knot with a given holonomy representation (called rho_2). There are essentially two boundary unipotent representations from the complement of the figure eight knot into PU(2,1), we call them rho_1 and rho_2. We make explicit some fundamen…

We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In particular, they may be used to give an explicit check that spherical braid grou…

Derives a formula for fermion dimensions in spherically symmetric monopole backgrounds.

Consider a three dimensional cusped spherical $\mathrm{CR}$ manifold $M$ and suppose that the holonomy representation of $π_1(M)$ can be deformed in such a way that the peripheral holonomy is generated by a non-parabolic element. We prove that, in this case, there is a spherical $\mathrm{CR}$ structure on some Dehn sur…

From the homotopy groups of two cubic spherical 3-manifolds we construct the isomorphic groups of deck transformations acting on the 3-sphere. These groups become the cyclic group of order eight and the quaternion group respectively. By reduction of representations from the orthogonal group to the identity representati…

Characterizes representations for complex projective structures with specific branch data.

Enhances Gaussian processes with spherical features for better scalability and flexibility.

The paper explores geometric properties of interception curves on planes and spheres.

Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…

Third-order PDEs describe spherical and pseudospherical surfaces.

We give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of G=O(n+1,1) and G'=O(n,1). We construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explic…

Paper introduces S3W distance for spherical probability distributions.

Generalizes string-net modular functors to non-spherical categories.

Proves a generalization of a multiplicity one theorem for specific groups.

Bayesian approach approximates probability functions of Gaussian mixtures.

DeepSphere improves spherical CNNs by balancing efficiency and rotation equivariance.

SRCA reduces high-dimensional data to lower dimensions while preserving geometric structures.

This paper connects Laguerre minimal surfaces to Weierstrass representations.

A new GP model uses spherical harmonics for faster inference.

Derives TAP approximation for Bayesian linear regression.

Researchers determine all possible representations of monodromy for Schwarzian equations on punctured surfaces.

In this paper, we focus on some characterizations for curves in the Galilean and Pseudo-Galilean space.

We study surfaces of constant positive Gauss curvature in Euclidean 3-space via the harmonicity of the Gauss map. Using the loop group representation, we solve the regular and the singular geometric Cauchy problems for these surfaces, and use these solutions to compute several new examples. We give the criteria on the …

The geometry of symmetric spaces, polar actions, isoparametric submanifolds and spherical buildings is governed by spherical Weyl groups and simple Lie groups. A natural generalization of semisimple Lie groups are affine Kac-Moody groups as they mirror their structure theory and have good explicitely known representati…

Study integral kernels on complex symmetric spaces and their Dyson Brownian Motion applications.

Minimal Morse functions on Poincaré dodecahedral space are selected via spectral properties.

A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories, and in this case the vector spaces agree with the state spaces of the correspondi…

This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of dist…

Paper proposes SMFN for high-res spherical video super-resolution.

Uniformizes CR structure on a specific 3-manifold.