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.
Explains the pure cactus group of degree three and its relation to four points on a circle.
A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant called the simplifying number. We show that branched covering surface-knots with degree three have the simplifying numbers less than three.
In this paper, we prove the Bounded Height Conjecture which the author formulated in [2]. As a corollary, it follows that there are only a finite number of hyperbolic three manifolds of bounded volume and trace field degree.
New bounds on Khovanov homology for positive links families.
New algebraic theory classifies symplectic curves in complex projective space.
We give an explicit formula for the projectively invariant quantization map between the space of symbols of degree three and the space of third-order linear differential operators, both viewed as modules over the group of diffeomorphisms and the Lie algebra of vector fields on a manifold.
Although it is known that the dimension of the Vassiliev invariants of degree three of long virtual knots is seven, the complete list of seven distinct Gauss diagram formulas have been unknown explicitly, where only one known formula was revised without proof. In this paper, we give seven Gauss diagram formulas to pres…
Upper bounds on map degrees for various manifold types.
We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.
In this paper, it is shown that every orientable closed 3-manifold maps with nonzero degree onto at most finitely many homeomorphically distinct irreducible non-geometric orientable closed 3-manifolds. Moreover, given any nonzero integer, as a mapping degree up to sign, every orientable closed 3-manifold maps with that…
Study reveals striking uniformity in triply graded link homology for specific braids.
A is an embedding of a graph on surfaces where every face has length three. In this article, we show the existence of contractible Hamiltonian cycle in triangulated maps of which minimum degree is four.
The problem of finding all minimal surfaces presented in parametric form as polynomials of certain degree is discussed by many authors. It is known that the classical Enneper surface is (up to position in space and homothety) the only polynomial minimal surface of degree 3 in isothermal parameters. In higher degrees th…
Develops a new tensor model for clustering with degree correction.
For ordinary knots in R3, there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual knots of increasing strength. We demonstrate that the strongest invariant …
We calculate Euclidean distance degrees for common manifold optimization types.
We prove that the unique least-perimeter way of partitioning the unit 2-dimensional disk into three regions of prescribed areas is by means of the standard graph consisting in three balanced constant geodesic curvature curves meeting themselves at 120 degrees, and reaching orthogonally the boundary of the disk.
Affine cactus groups are CAT(0) and hyperbolic.
Withdrawn by the author in favour of math.GT/0511602
New hexagonal circular 3-webs with reducible curves classified.
Paper studies minimal surfaces in curved spaces, proving existence and properties.
The Milnor degree of a 3-manifold is an invariant that records the maximum simplicity, in terms of higher order linking, of any link in the 3-sphere that can be surgered to give the manifold. This invariant is investigated in the context of torsion linking forms, nilpotent quotients of the fundamental group, Massey pro…
A connected combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. A connected combinatorial 2-manifold is called weakly regular if it has a vertex-transitive automorphism group. Clearly, a weakly regular combinatorial 2-manifold is degree-regular and a degree-regular combinator…
Three-layer neural networks learn hierarchical polynomial functions efficiently.
Cryptocurrency is a well-developed blockchain technology application that is currently a heated topic throughout the world. The public availability of transaction histories offers an opportunity to analyze and compare different cryptocurrencies. In this paper, we present a dynamic network analysis of three representati…
We study the map degrees between quasitoric 4-manifolds. Our results rely on Theorems proved by Duan and Wang. We determine the set D (M, N) of all possible map degrees from M to N when M and N are certain quasitoric 4-manifolds. The obtained sets of integers are interesting, e. g. those representable as the sum of two…
In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees -cohomology with $\C/\Z$-cohomology, for . Furthermore, they are shown to be rigid in a variation of paths (p…
We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2 with locally free tangent sheaves, and show that codimension one distr…
Paper analyzes a three-loop linkage, showing it's overconstrained and shaky.
Discover new identities linking hypersurface mean curvatures.
The paper argues for using more degrees of freedom in empirical financial analysis to improve conclusions.
This paper introduces the notion of ``relative gerbes'' for smooth maps of manifolds, and discusses their differential geometry. The equivalence classes of relative gerbes are further classified by the relative integral cohomology in degree three.
Matveev and Piergallini independently showed that, with a small number of known exceptions, any triangulation of a three-manifold can be transformed into any other triangulation of the same three-manifold with the same number of vertices, via a sequence of 2-3 and 3-2 moves. We can interpret this as showing that the Pa…
Symmetry-breaking in three differential geometry conjectures.
We show how the space of complex spin structures of a closed oriented three-manifold embeds naturally into a space of quadratic functions associated to its linking pairing. Besides, we extend the Goussarov-Habiro theory of finite type invariants to the realm of compact oriented three-manifolds equipped with a complex s…
New method explains computational barriers in high-dimensional statistical models.
Degenerate solutions found in 2D H-system bubbles with higher degrees.
We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form 120 degree angles, and expands homothetically under curve shortening…
We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In parti…
We establish the existence of an integer degree for the natural projection map from the space of parameterizations of asymptotically conical self-expanders to the space of parameterizations of the asymptotic cones when this map is proper. As an application we show that there is an open set in the space of cones in the …
For a branched cover between two closed orientable surfaces, the Riemann-Hurwitz formula relates the Euler characteristics of the surfaces, the total degree of the cover, and the total length of the partitions of the degree given by the local degrees at the preimages of the branching points. A very old problem asks whe…
Let be a closed, oriented and smooth manifold of dimension . Let be the space of smooth loops in . Chas and Sullivan introduced loop product, a product of degree on the homology of . In this paper we show how for three manifolds the ``nontriviality'' of the loop product relates to the ``hyperbol…
We introduce Dolbeault cohomology valued characteristic classes of Higgs bundles over complex manifolds. Flat vector bundles have characteristic classes lying in odd degree de Rham cohomology and a theorem of Reznikov says that these must vanish in degrees three and higher over compact Kähler manifolds. We provide a si…
We explain some interesting relations in the degree three bounded cohomology of surface groups. Specifically, we show that if two faithful Kleinian surface group representations are quasi-isometric, then their bounded fundamental classes are the same in bounded cohomology. This is novel in the setting that one end is d…
This paper adresses the following problem: Given a closed orientable three-manifold M, are there at most finitely many closed orientable three-manifolds 1-dominated by M? We solve this question for the class of closed orientable graph manifolds. More presisely the main result of this paper asserts that any closed orien…
Researchers study chirality in a specific type of torus-covering link.
GCNs favor high-degree nodes, leading to biased performance; a new method mitigates this.
This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). Integrability corresponds to the existence of many submanifolds that are spanned by lines in the cones. These GL(2)-stru…