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.
The study characterizes embeddable 2-complexes in 3-space.
Every 4-manifold can be smoothly embedded in complex projective 3-space.
We characterise the embeddability of simply connected locally 3-connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of Lovász, Pardon and Wagner.
Novel Jones polynomial for open curves in 3D space.
In 1900, Macfarlane proposed a hyperbolic variation on Hamilton's quaternions that closely resembles Minkowski spacetime. Viewing this in a modern context, we expand upon Macfarlane's idea and develop a model for real hyperbolic 3-space in which both points and isometries are expressed as complex quaternions, analogous…
We prove that 2-dimensional simplicial complexes whose first homology group is trivial have topological embeddings in 3-space if and only if there are embeddings of their link graphs in the plane that are compatible at the edges and they are simply connected.
Defines Vassiliev complexity measures for open and closed curves in 3D space.
We introduce dual matroids of 2-dimensional simplicial complexes. Under certain necessary conditions, duals matroids are used to characterise embeddability in 3-space in a way analogous to Whitney's planarity criterion. We further use dual matroids to extend a 3-dimensional analogue of Kuratowski's theorem to the class…
The paper proves a rigidity theorem for non-compact convex sets in hyperbolic 3-space.
Complete classification of homogeneous real hypersurfaces in complex 3-space.
This paper is the last paper in a series of five papers. Building on earlier papers in this series, we prove an analogue of Kuratowski's characterisation of graph planarity for three dimensions. More precisely, a simply connected 2-dimensional simplicial complex embeds in 3-space if and only if it has no obstruction fr…
New invariants measure entanglement of open curves in 3D space.
Engel structures on bundles over 3-manifolds in complex 3-space.
Study symmetries in smoothed polygonal links.
Equivalences between conformal foliations on Euclidean -space, Hermitian structures on Euclidean -space, shear-free ray congruences on Minkowski -space, and holomorphic foliations on complex -space are explained geometrically and twistorially; these are used to show that 1) any real-analytic complex-valued …
Study modular surfaces in Lorentz-Minkowski 3-space, classifying and analyzing their curvature and applications.
Unified framework for Alexandrov 3-spaces, extending manifold results.
The paper explores affine geometry of line congruences using singularity theory.
We show existence of constant mean curvature 1 surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter 3-space, but with a different non-embedded end behavior.
New knot models analyze local entanglement for robust curve analysis.
We describe the relationship between complex-valued harmonic morphisms from Minkowski 4-space} and the shear-free ray congruences of mathematical physics. Then we show how a horizontally conformal submersion on a domain of Euclidean 3-space gives the boundary values at infinity of a complex-valued harmonic morphism on …
In this paper, we firstly introduce the group of similarity transformations in the Minkowski-3 space. We describe differential- geometric invariants of a non-lightlike curve according to the group of similarity transformations of the Minkowski 3-space. We show extension of fundamental theorem for non-lightlike curves u…
We make observations about constant mean curvature surfaces in Euclidean 3-space and their dual surfaces, and the resulting pairs of surfaces in hyperbolic 3-space under the Lawson correspondence.
It is shown that timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL(2,R) via Bryant type representation formulae. These formulae are used to investigate an explicit one-to-one correspondence, the s…
3D analog of Whitney's planarity criterion for 2-complexes.
Sharp inequality proved in 3D hyperbolic spaces using flow methods.
We construct triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space, with the same topology as the triply periodic minimal surfaces in the Euclidean 3-space, called Schwarz rPD surfaces.
We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.
Classifies surfaces with special curvature properties.
The paper characterizes timelike rectifying curves in De Sitter 3-space.
Study on minimal surfaces in a 3D space with 2m-norm.
We study the symplectic geometry of the moduli space of closed n-gons with fixed side-lengths in hyperbolic 3-space. We prove that these moduli spaces have a symplectic structure coming from Poisson Lie theory. We construct completely integrable systems on these moduli spaces by bending n-gons along their diagonals. Th…
Survey Bernstein-type theorems for graphical surfaces in Euclidean and Lorentz-Minkowski spaces.
Study bifurcations of curves on surfaces in Minkowski 3-space.
We give a conformal representation in terms of meromorphic data for a certain class of spacelike surfaces in the Lorentz-Minkowski 4-space L^4 whose mean curvature vector is either lightlike or zero at each point. This representation extends simultaneously the Weierstrass representation for minimal surfaces in Euclidea…
By a fixed continuous map from a -space to itself, a knot in the -space may be mapped to another knot in the -space. We analyze possible knot types of them. Then we map a knot repeatedly by a fixed continuous map and analyze possible infinite sequences of knot types.
Paper proves a theorem about constant mean curvature surfaces in isotropic 3-space.
Solves four problems related to sphere families in 3D space.
The study identifies surfaces with Maslovian normal bundles.
Motivated by the beautiful theory and the rich applications of harmonic conformal immersions and conformal immersions of constant mean curvature (CMC) surfaces, we study biharmonic conformal immersions of surfaces into a generic 3-manifold. We first derive an invariant equation for such immersions, we then try to answe…
Constructs graphs with singularities in a special space.
The paper proves shellability is hard for d-balls when d is at least 3.
In this paper we study lightlike surfaces of Minkowski 3- space such that they have degenerate or non-degenerate planar normal sections. We first show that every lightlike surface of Minkowski space has degenerate planar normal sections. Then we study lightlike surfaces with non-degenerate planar normal sections a…
A correspondence is studied by H. Matsuda between front projections of Legendrian links in the standard contact structure for 3-space and rectangular diagrams. In this paper, we introduce braided rectangular diagrams, and study a relationship with Legendrian links in the standard contact structure for 3-space. We show …
New framework for zero mean curvature surfaces in isotropic 3-space.
New BDEs reveal singular surfaces from line congruences.
We define discrete flat surfaces in hyperbolic 3-space from the perspective of discrete integrable systems and prove properties that justify the definition. We show how these surfaces correspond to previously defined discrete constant mean curvature 1 surfaces in hyperbolic 3-space, and we also describe discrete focal …
We investigate the close relationship between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. Just as in the case of minimal surfaces in Euclidean 3-space, the only complete connected embedded constant mean curvature 1 surfaces with two ends in hyperbolic space are we…