Related papers: Formal punctured ribbons and two-dimensional local…

This paper is concerned with developing a 2-dimensional analogue of the notion of an ordinary discrete fibration. A definition is proposed, and it is shown that such discrete 2-fibrations correspond via a 2-equivalence to certain…

This paper demonstrates that parallel vector curves are piecewise cubic rational curves in 3D piecewise linear vector fields. Parallel vector curves -- loci of points where two vector fields are parallel -- have been widely used to extract…

We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We…

We present local biplots, a an extension of the classic principal components biplot to multi-dimensional scaling. Noticing that principal components biplots have an interpretation as the Jacobian of a map from data space to the principal…

The family of Euclidean triangles having some fixed perimeter and area can be identified with a subset of points on a nonsingular cubic plane curve, i.e., an elliptic curve; furthermore, if the perimeter and the square of the area are…

We introduce the notion of a ribbon-clasp surface-link, which is a generalization of a ribbon surface-link. We generalize the notion of a normal form on embedded surface-links to the case of immersed surface-links and prove that any…

A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we…

A rope is a non-singular embedding of a closed interval into R^3, which sends the ends of the interval to some fixed points A and B such that |AB|=1. A rope is short if its length is less than 3. The main result of the paper is that the…

A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.

In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected via a prescribed number of iterations and symbolic…

We characterise when a set of simple closed curves in an orientable surface forms a bouquet, in terms of relations between the corresponding Dehn twists.

Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but…

A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…

Relative notions of combinatorial asphericity have been used to prove that injective labeled oriented trees (which encode spines of ribbon 2-knots) are aspherical. This article presents an overview and comparison of the different notions of…

Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local…

A parallelogram is conformally inscribed in four lines in the plane if it is inscribed in a scaled copy of the configuration of four lines. We describe the geometry of the three-dimensional Euclidean space whose points are the…

We show several geometric and algebraic aspects of a necklace: a link composed with a core circle and a series of circles linked to this core. We first prove that the fundamental group of the configuration space of necklaces (that we will…

One distinguishing feature of rational curves is that they have algebraic parameterizations. Arc spaces are a way of describing approximations to parameterizations of all curves in some fixed space. Playing on these descriptions, this paper…