A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study rigidity and volume optimization of hyperbolic polyhedra.
We give a unified description of tetrahedra with lightlike faces in 3d anti-de Sitter, de Sitter and Minkowski spaces and of their duals in 3d anti-de Sitter, hyperbolic and half-pipe spaces. We show that both types of tetrahedra are determined by a generalized cross-ratio with values in a commutative 2d real algebra t…
We provide a detailed proof of the following folklore theorem: Let mu > 0 be a Margulis constant for 3-dimensional hyperbolic space. Then for any d>0 there exists a constant K>0, depending on mu and d, so that for any complete finite volume hyperbolic 3-manifold M, the d-neighborhood of the mu-thick part of M can be tr…
Geodesic loops on tetrahedra are studied in spherical and hyperbolic spaces.
The paper connects quantum -symbols to tetrahedra volumes via discrete Fourier transforms.
We extend the definition of curvature homogeneity of type (1,3) to include the possibility that there is a homothety between any two points of a manifold preserving the first r covariant derivatives of the curvature operator simultaneously; we call this strong curvature homogeneity of type (1,3) up to order r. We chara…
Simple geodesics on spherical tetrahedra identified for specific angles.
We present a generalization of Minkowski's classic theorem on the reconstruction of tetrahedra from algebraic data to homogeneously curved spaces. Euclidean notions such as the normal vector to a face are replaced by Levi-Civita holonomies around each of the tetrahedron's faces. This allows the reconstruction of both s…
Survey on geodesics on tetrahedra in curved spaces.
The paper defines new homotopy relations on knot projections and classifies certain knot types.
Consider a 3dimensional manifold obtained by gluing a finite number of ideal hyperbolic tetrahedra via isometries along their faces. By varying the isometry type of each tetrahedron but keeping fixed the gluing pattern we define a space of complete hyperbolic metrics on with cone singularities …
We compute for all orientable irreducible geometric 3-manifolds certain complexity functions that approximate from above Matveev's natural complexity, known to be equal to the minimal number of tetrahedra in a triangulation. We can show that the upper bounds on Matveev's complexity implied by our computations are sharp…
In this study, we define some new types of non-null ruled surfaces called slant ruled surfaces in the Minkowski 3-space E_1^3. We introduce some characterizations for a non-null ruled surface to be a slant ruled surface in E_1^3. Moreover, we obtain some corollaries which give the relationships between a non-null slant…
The paper proves a Minkowski-like theorem for tetrahedra in dS3 and AdS3.
Randomly glued tetrahedra form connected 3-manifolds with a single boundary.
The present paper follows the computational approach to 3-manifold classification via edge-coloured graphs, already performed by several authors with respect to orientable 3-manifolds up to 28 coloured tetrahedra, non-orientable 3-manifolds up to 26 coloured tetrahedra, genus two 3-manifolds up to 34 coloured tetrahedr…
Motivated by the Turaev-Viro invariant of 3-manifolds, we construct a formal topological invariant of closed, oriented 3-manifolds involving spherical tetrahedra as an application of the asymptotic formula of 6j symbols for the Quantum Enveloping Algebra of sl(2). This invariant can be considered as a spherical version…
Quaternionic curves with specific torsion properties don't exist.
We classify the orientable finite-volume hyperbolic 3-manifolds having non-empty compact totally geodesic boundary and admitting an ideal triangulation with at most four tetrahedra. We also compute the volume of all such manifolds, we describe their canonical Kojima decomposition, and we discuss manifolds having cusps.…
Researchers found the minimum number of tetrahedra needed to triangulate elliptic and sol 3-manifolds.
Researchers found the Wigner derivative and its inverse are equal for spherical tetrahedra.
In the paper we define a "volume" for simplicial complexes of flag tetrahedra. This generalizes and unifies the classical volume of hyperbolic manifolds and the volume of CR tetrahedra complexes. We describe when this volume belongs to the Bloch group. In doing so, we recover and generalize results of Neumann-Zagier, N…
Hyperideal tetrahedra are the fundamental building blocks of hyperbolic 3-manifolds with geodesic boundary. The study of their geometric properties (in particular, of their volume) has applications also in other areas of low-dimensional topology, like the computation of quantum invariants of 3-manifolds and the use of …
We give a rigorous geometric proof of the Murakami-Yano formula for the volume of a hyperbolic tetrahedron. In doing so, we are led to consider generalized hyperbolic tetrahedra, which are allowed to be non-convex, and have vertices `beyond infinity'; and we uncover a group, which we call 22.5K, of 23040 scissors-class…
Hyperbolic links in thickened torus decompose into angled tetrahedra.
We analyze the dynamical properties of a tetrahedron transformation on the space of non-degenerate tetrahedra which can be identified with the non-compact globally symmetric -dimensional space $\mbox{Sl}(3,\mathbb{R}) / \mbox{So}(3,\mathbb{R})$. We establish the existence of a local attractor which coincides with th…
Researchers found a spinorial representation for surfaces in 3D Lorentzian spaces.
We describe the deformation space of a solid torus with boundary modelled on convex ideal hyperbolic polyhedra. This deformation space is given by natural Gauss--Bonnet type inequalities on the dihedral angles. The result extends to solid tori with an arbitrary conical singularity along the core. Our method is to decom…
We construct new topological invariants of three-dimensional manifolds which can, in particular, distinguish homotopy equivalent lens spaces L(7,1) and L(7,2). The invariants are built on the base of a classical (not quantum) solution of pentagon equation, i.e.algebraic relation corresponding to a ``2 tetrahedra to 3 t…
We improve and extend to the non-orientable case a recent result of Karabas, Malicki and Nedela concerning the classification of all orientable prime 3-manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra.
Census of 10-tetrahedra hyperbolic 3-manifolds with 150,730 new examples.
Study laws of cosines and sines for hyperbolic shapes with ideal vertices.
We obtained a complete classification of simple closed geodesics on regular tetrahedra in Lobachevsky space. Also, we evaluated the number of simple closed geodesics of length not greater than and found the asymptotic of this number as goes to infinity.
A generalized hyperbolic tetrahedra is a polyhedron (possibly non-compact) with finite volume in hyperbolic space, obtained from a tetrahedron by the polar truncation at the vertices lying outside the space. In this paper it is proved that a volume formula for ordinary hyperbolic tetrahedra devised by J. Murakami and M…
Study geometry of tetrahedra in complex hyperbolic space and Hilbert spaces.
The paper studies the face angles of tetrahedra with a fixed base.
Study - symbols linking anti-de Sitter tetrahedra to hyperbolic geometry.
Method samples triangulations of manifolds using biased random walks.
Starting with an ideal triangulation of the interior of a compact 3-manifold M with boundary, no component of which is a 2-sphere, we provide a construction, called an inflation of the ideal triangulation, to obtain a strongly related triangulations of M itself. Besides a step-by-step algorithm for such a construction,…
In this paper we provide the first examples of non-flat soap films proven to span tetrahedra. These are members of a continuous two parameter family of soap films with tetrahedral boundaries. Of particular interest is a two parameter subfamily where each spanning soap film has the property that two minimal surfaces mee…
Characterizes billiard and quasigeodesic flows in polyhedral convex bodies.
From its creation in 1989 through subsequent extensions, the widely-used "SnapPea census" now aims to represent all cusped finite-volume hyperbolic 3-manifolds that can be obtained from <= 8 ideal tetrahedra. Its construction, however, has relied on inexact computations and some unproven (though reasonable) assumptions…
In this paper, by the studying of the Gauss map, Laplacian operator, curvatures of surfaces in and Bour's theorem, we are going to identify surfaces of revolution with pointwise 1-type Gauss map property in dimensional Minkowski space.
New algorithm tackles non-stationary RL with near-optimal regret bounds.
The paper classifies surfaces with constant curvature in 3D De Sitter and anti De Sitter spaces.
The paper sharpens inequalities in hyperbolic spaces.
We identify a region $\Bbb{W}_{\f{1}{3}}$ in a Grassmann manifold $\grs{n}{m}$, not covered by a usual matrix coordinate chart, with the following important property. For a complete submanifold in $\ir{n+m} \, (n\ge 3, m\ge2)$ with parallel mean curvature whose image under the Gauss map is contained in a compact su…
Given a combinatorial description of a polyhedron having edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize is generally not a convex subset of \cite{DIAZ}. If has five or more faces, Andreev's Theorem states that the corresponding space of dihedral angle…