arXiv research

The hyperbolic dodecahedral space is cubulated and covered with special properties.

Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes…

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

Researchers prove Seifert-Weber dodecahedral space is an L-space.

In this paper we settle Thurston's old question of whether the Weber-Seifert dodecahedral space is non-Haken, a problem that has been a benchmark for progress in computational 3-manifold topology over recent decades. We resolve this question by combining recent significant advances in normal surface enumeration, new he…

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…

6 out of 29 dodecahedral 3-spheres are L-spaces, solving a Seiberg-Witten question.

In a flat space, the global topology of comoving space can induce a weak acceleration effect similar to dark energy. Does a similar effect occur in the case of the Poincare dodecahedral space S^3/I^*? Does the effect distinguish the Poincare space from other well-proportioned spaces? The residual acceleration effect in…

If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal cup-length, then for any riemannian metric g on M, we show that the systole Sys(M,g) and the volume Vol(M,g) of the riemannian manifold (M,g) are related by the following isosystolic inequality: Sys(M,g)^n \leq n! Vol(M,g). The …

We show that for certain arithmetic groups, geometrically finite subgroups are the intersection of finite index subgroups containing them. Examples are the Bianchi groups and the Seifert-Weber dodecahedral space. In particular, for manifolds commensurable with these groups, immersed incompressible surfaces lift to embe…

In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the $3$-sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic reflection orbifolds admit hidden symmetries, and we verify the Neumann-Reid con…

We prove that an irreducible 3-manifold whose fundamental group satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber …

The only finite nonabelian simple group acting on a homology 3-sphere - necessarily non-freely - is the dodecahedral group $\Bbb A_5 \cong {\rm PSL}(2,5)$ (in analogy, the only finite perfect group acting freely on a homology 3-sphere is the binary dodecahedral group $\Bbb A_5^* \cong {\rm SL}(2,5)$). In the present pa…

Machine learning speeds up the construction of virus assembly fitness landscapes.

New findings show fundamental group is not audible in spherical space forms.

The study finds infinitely many counterexamples to a generalized Double Soul Conjecture.

New curvature positivity helps classify spherical spaces and complex projective spaces.

Study on generalized spherical surfaces in Euclidean spaces.

Minimal surfaces in spherical space forms have limited genus.

In this paper we consider the spherical slant helices in $R^3$. More- over, we show how could be obtained to a spherical slant helix and we give some spherical slant helix examples in Euclidean 3-space.

Study spherical surfaces with conical points, proving systole inequality.

Researchers find highest volumes for isospectral spherical orbifolds and space forms.

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…

Study on metrics with positive scalar curvature on spherical space forms.

In this paper, we give definitions and characterizations of normal and spherical curves in the dual space. We show that normal curves are also spherical curves in D^3.

The paper explores integral formulas and behavior of spherical functions.

Study spherical images of modified vector fields on a unit sphere.

DELIMIT PyTorch enhances deep learning for diffusion imaging.

Timelike geometry of spherical simplices is shown to be isometric to vector spaces.

New classification of spherical 2-Dupin submanifolds.

The paper proves stability of inequalities for nearly spherical sets in various spaces.

Study local features of decorated representation spaces for spherical surfaces.

Study spherical convex bodies using $L_p$-floating areas and curvature entropy.

This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$ ($κ>0$) and $H_\k^3$ ($κ<0$), to the standard {\itshape spherical wav…

Locally classifies 4D spherical symmetric Finsler spaces.

Study null surfaces of pseudo-spherical curves in anti-de Sitter space.

String-net models explore non-spherical fusion categories, revealing new spin structures and representations.

Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.

Study pseudo-spherical submanifolds with 1-type Gauss map in pseudo-spheres.

We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems.

Proves rigidity for higher rank three-manifolds without curvature constraints.

Proposes spherical text embedding for better directional similarity.

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…

Characterizes curves on geodesic spheres and totally geodesic hypersurfaces in hyperbolic and spherical spaces.

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.

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

Study Froyshov invariants and closed geodesics in hyperbolic 3-manifolds.

Dunkl connections on complex plane don't preserve metrics.