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 paper describes distances on Sol-type groups using novel geometric techniques.
New method finds metrics on surfaces with prescribed curvatures using circle packings and surgery.
Contradicts claims about Poincaré complexes and homology manifolds.
Divide knots and links, defined by A'Campo in the singularity theory of complex curves, is a method to present knots or links by real plane curves. The present paper is a continuation of the author's previous result that every knot in the major subfamilies of Berge's lens space surgery (i.e., knots yielding a lens spac…
It is proved that every knot in the major subfamilies of J. Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped (real) plane curve as a "divide knot" defined by N. A'Campo in the context of singularity theory of complex curves. For each knot given by Berge's parame…
We show that every smooth closed curve C immersed in Euclidean 3-space satisfies the sharp inequality 2(P+I)+V >5 which relates the numbers P of pairs of parallel tangent lines, I of inflections (or points of vanishing curvature), and V of vertices (or points of vanishing torsion) of C. We also show that 2(P'+I)+V >3, …
We study collections of curves in generic position on a closed surface whose complement consists of one disk only, up to orientation-preserving homeomorphism of the surface. We define a surgery operation on the set of such collections and prove that any two of them can be connected by a sequence of such surgeries.
We discuss the properties of a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold, known as Luttinger's surgery, and use this construction to provide a purely topological interpretation of a non-isotopy result for symplectic plane curves with cusp and node singularities due to Moishezon.
A surgery classification theory is introduced for manifolds of bounded geometry up to quasi-isometry. The Borel conjecture for this theory is proven for flat Euclidean space.
For the purposes of this paper, Dehn surgery along a curve K in a 3-manifold M with slope r is `exceptional' if the resulting 3-manifold M_K(r) is reducible or a solid torus, or the core of the surgery solid torus has finite order in the fundamental group of M_K(r). We show that, providing the exterior of K is irreduci…
Study on knot surgeries reveals infinite residue characteristics and infinite order points.
Geometrically, Legendrian surfaces related by surgery have related skein-valued cluster spaces.
Algorithm converts curves on ribbon surfaces to contact surgery diagrams.
New Heegaard Floer homology findings block chirally cosmetic surgeries.
We prove that a sufficiently large surgery on any algebraic link is an L-space. For torus links we give a complete classification of integer surgery coefficients providing L-spaces.
This paper restricts efficient geodesics to non-separating curves.
The study explores Bertrand and Mannheim curves in 4D Euclidean space for framed curves.
This paper constructs Seifert-fibered Dehn surgeries for hyperbolic tunnel-number-one knots.
The paper discusses algorithms for reconstructing curves with given Euclidean or affine curvatures.
New proof shows most thin knots satisfy Cabling Conjecture.
In this paper we deal with curves with degeneration degree two in pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the dimensional pseudo-Euclidean space of index two. Also we characte…
In [18], L. R. Pears proved that Bertrand curves in E-n(n > 3) are degenerate curves. This result restate in [16] by Matsuda and Yorozu. They proved that there is no special Bertrand curves in E-n(n > 3) and they define new kind of Bertrand curves called (1, 3)-type Bertrand curves in 4-dimensional Euclidean space. In …
In this paper we introduce a new geometric flow --- the hyperbolic gradient flow for graphs in the -dimensional Euclidean space . This kind of flow is new and very natural to understand the geometry of manifolds. We particularly investigate the global existence of the evolution of convex hypers…
The paper studies circular evolutes and involutes of framed curves in Euclidean space.
Knot Floer homology is reinterpreted as immersed curves.
Quasiregular curves are Hölder continuous and have higher integrability.
In this paper, we introduce the quaternionic similar curves in 4-dimensional Euclidean space. We show that the families of quaternionic curves with vanishing curvatures form the families of quaternionic similar curves.
In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We characterize rectifying curves in the -dimensional Euclidean space in different ways…
In this study, we consider curves of generalized AW(k)-type of Euclidean n-space. We give curvature conditions of these kind of curves.
Paper defines curvature equivalence for Legendre curves in a plane.
In this paper, we investigate Mannheim pairs, Frenet-Mannheim curves and Weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space(E 3 ). We obtain some characterizations of these curves.
Computing uniformization maps for surfaces has been a challenging problem and has many practical applications. In this paper, we provide a theoretically rigorous algorithm to compute such maps via combinatorial Calabi flow for vertex scaling of polyhedral metrics on surfaces, which is an analogue of the combinatorial Y…
The study examines Bertrand Legendre curves in the unit tangent bundle over Euclidean plane.
We study Weinstein 4-manifolds which admit Lagrangian skeleta given by attaching disks to a surface along a collection of simple closed curves. In terms of the curves describing one such skeleton, we describe surgeries that preserve the ambient Weinstein manifold, but change the skeleton. The surgeries can be iterated …
Ozsváth-Szabó proved the property that any coefficient of Alexander polynomial of lens space knot is either or and the non-zero coefficients are alternating. Combining the formulas of the Alexander polynomial of lens space knots due to Kadokami-Yamada and Ichihara-Saito-Teragaito, we refine Ozsváth-Szabó's p…
Researchers identify graph components for unicellular collections.
In this paper, we study helices and the Bertrand curves. We obtain some of the classification results of these curves with respect to the modified orthogonal frame in Euclidean 3-spaces.
Veering branched surfaces help construct geodesic flows on curved surfaces.
In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the first time in 4-dimensional Euclidean space. Then we obtain the conditio…
In [5], Matsuda and Yorozo obtained that Mannheim curves in 4-dimensional Euclidean space. In this study, we define quaternionic Mannheim curves and we give some characterizations of them in Euclidean 3-space and 4-space.
In this study, we try to semi-real quaternionic curves in the semi-Euclidean space E_2^4. Firstly, we introduce algebraic properties of semi-real quaternions. And then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E_2^4. Lastly, we illustrate some examples…
In this study we consider AW(k)-type curves according to parallel transport frame in Euclidean space E^4. We give the relations between the parallel transport curvatures of these kinds of curves.
We prove that the curve graph $\calC^{(1)}(S)$ is Gromov-hyperbolic with a constant of hyperbolicity independent of the surface . The proof is based on the proof of hyperbolicity of the free splitting complex by Handel and Mosher, as interpreted by Hilion and Horbez.
The study examines vertices in curves with singular points in the Euclidean plane.
The paper studies singularities on parallels of tangent developable surfaces of frontal curves.
Study rectifying curves in 3D multiplicative Euclidean space.
Paper proves uniqueness of bridge multisections for surfaces in 4-space.
New parametrizations for minimal timelike surfaces discovered.