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.
Asymptotic dimension of planes and graphs is at most three.
Paper introduces clock moves for plane graphs and proves Alexander polynomial properties.
New combinatorial type helps distinguish plane curve topologies.
Study Morse functions on projective plane using Reeb graphs.
For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane closed curve whose chord diagram contains the given chord diagram as a sub-chord diagram. For any generic immersion of the complete graph on six vertices to t…
The aim of this work is studying translating graphs by mean curvature flow in $\Real^3$. We prove non-existence of complete translating graphs over bounded domains in $\Real^2$. Furthermore, we show that there are only three types of complete translating graphs in $\Real^3$; entire graphs, graphs between two vertical p…
We give an explicit calculation of the Wu invariants for immersions of a finite graph into the plane and classify all generic immersions of a graph into the plane up to regular homotopy by the Wu invariant. This result is a generalization of the fact that two plane curves are regularly homotopic if and only if they hav…
Develops a method to construct entire minimal graphs of odd dimensions.
The splitting number is effective to distinguish the embedded topology of plane curves, and it is not determined by the fundamental group of the complement of the plane curve. In this paper, we give a generalization of the splitting number, called the splitting graph. By using the splitting graph, we classify the embed…
Kronheimer-Mrowka's instanton homology dimension equals Tait colorings.
Study of Poincaré-Reeb graphs for algebraic domains.
3D manifolds can map to a plane with specific curve patterns.
The paper explores winding numbers of almost embeddings of a 4-vertex graph in the plane.
There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedd…
Odd crossing numbers and even rotation numbers for cycles in plane immersions.
We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomials of some series of spatial graphs are dense in a certain region in …
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
Study Steklov eigenvalues on hyperbolic triangle-tiling graphs.
Study inverse curve shortening flow on hyperbolic plane, classifying solitons.
Generalizes Kauffman's clock theorem to surfaces.
The ray graph is a Gromov hyperbolic graph on which the mapping class group of the plane minus a Cantor set acts by isometries. We give a description of the Gromov boundary of the ray graph in terms of cliques of long rays on the plane minus a Cantor set. As a consequence, we prove that the Gromov boundary of the ray g…
Study shows stable graphs in Heisenberg group are essentially planes.
A mathematical paradox shows secant planes don't always form a tangent plane, but some analogies hold with a specific vector product.
We consider here 6-regular plane graphs whose faces have size 1, 2 or 3. In Section 2 a practical enumeration method is given that allowed us to enumerate them up to 53 vertices. Subsequently, in Section 3 we enumerate all possible symmetry groups of the spheres that showed up. In Section 4 we introduce a new Goldberg-…
Infinite clique of rays in plane minus Cantor set.
The paper defines invariants for almost graph embeddings and explores their properties.
A plane graph is a {\em plane minor} of a plane graph if there is a sequence of vertex and edge deletions, and edge contractions performed on the plane, that takes to . Motivated by knot theory problems, it has been asked if the plane minor relation is a well-quasi-order. We settle this in the affirmativ…
The paper explores invariants of graph drawings in the plane.
This paper discusses reformulations of the problem of coloring plane maps with four colors. We give a number of alternate ways to formulate the coloring problem including a tautological expansion similar to the Penrose Bracket, and an extension of the Penrose Bracket that counts colorings of arbitrary cubic graphs pres…
Well-quasi-orders proved on embedded planar graphs.
New examples of mixed-type zero-curvature graphs found.
A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face. A railroad in a plane graph is a circuit of hexagonal faces, such that any hexagon is adjacent to its neighbors on opposite edges. A graph without a railroad is called tight. We consider the zigz…
We construct harmonic diffeomorphisms from the complex plane onto any Hadamard surface whose curvature is bounded above by a negative constant. For that, we prove a Jenkins-Serrin type theorem for minimal graphs in over domains of bounded by ideal geodesic polygons and show the existence of a se…
The study examines stationary integral varifolds near multiplicity 2 planes, proving regularity under specific conditions.
The paper characterizes graph manifolds using fold maps and embeddability of polyhedra.
Study on factorizations of knot polynomials for up to 12 crossings.
We obtain a criterion for approximability by embeddings of piecewise linear maps of a circle to the plane, analogous to the one proved by Minc for maps of a segment to the plane. Theorem. Let S be a triangulation of a circle with s vertices. Let f be a simplicial map of the graph S to the plane. The map f is approximab…
Examines discrete curvature's relation to smooth curvature in 3 spaces.
Every cubic graph is a bridge trisection's 1-skeleton for a knotted surface.
Paper extends Enami-Ozeki-Yamaguchi's work on planar quadrangulations.
It is classically known that the only zero mean curvature entire graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space is called of mixed type if it changes causal type from space-like to time-like. In , Osamu Kobayashi found …
We construct a Legendrian version of Envelope theory. A tangential family is a 1-parameter family of rays emanating tangentially from a smooth plane curve. The Legendrian graph of the family is the union of the Legendrian lifts of the family curves in the projectivized cotangent bundle . We study the singular…
Calabi's Bernstein-type theorem asserts that a zero mean curvature entire graph in Lorentz-Minkowski space which admits only space-like points is a space-like plane. Using the fluid mechanical duality between minimal surfaces in Euclidean 3-space and maximal surfaces in Lorentz-Minko…
We survey the construction and properties of the Yamada polynomial of spatial graphs and present the Yamada polynomial formulae for some classes of graphs. Then we construct an infinite family of spatial graphs for which roots of Yamada polynomials are dense in the complex plane.
A meander of order n is a simple closed curve in the plane which intersects a horizontal line transversely at 2n points. (Meanders which differ by an isotopy of the line and plane are considered equivalent.) Let Gamma_n be the Cayley graph of the symmetric group S_n as generated by all (n choose 2) transpositions. Let …
Rotation systems can't always be drawn in surfaces.
We obtain an optimal estimate for the extrinsic curvature of an entire minimal graph in $\H^2\times\R$, $\H^2$ the hyperbolic plane.
In this note we prove that every two-dimensional entire Willmore graph in with square integrable mean curvature is a plane.