Related papers: A model of the cubic connectedness locus
We describe a locally connected model of the boundary of the cubic connectedness locus. The model is obtained by constructing a decomposition of the space of critical portraits and collapsing elements of the decomposition into points. This…
Given a real algebraic curve in the projective 3-space, its hyperbolicity locus is the set of lines with respect to which the curve is hyperbolic. We give an example of a smooth irreducible curve whose hyperbolicity locus is disconnected…
We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…
We classify the planar cubic Cayley graphs of connectivity 2, providing an explicit presentation and embedding for each of them. Combined with [9] this yields a complete description of all planar cubic Cayley graphs.
We provide a mathematical model for the capability approach.
We prove a connectedness result for products of weighted projective spaces.
A solution to the problem of topological classification of real cubic fourfolds is presented. It is shown that the real locus of a real non-singular cubic fourfold is obtained from a projective 4-space either by adding several trivial one-…
We construct relatively bounded toroidal and toric models of relatively bounded fibrations over curves.
In this short note, a topos - called the topos of the connectivity space - is associated with every such space.
Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.
Given fixed distinct points $A, B, C, D$, we examine properties of the locus of points $X$ for which $(XA, XC)$, $(XB, XD)$ are isogonal. This locus is a cubic curve circumscribing $ABCD$. We characterize all possible such cubics $\mathcal…
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…
We survey some results on toric topology.
We give a method for searching for thin positions of a given link.
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
We address various topologies (de Bruijn, chordal ring, generalized Petersen, meshes) in various ways ( isometric embedding, embedding up to scale, embedding up to a distance) in a hypercube or a half-hypercube. Example of obtained…
In this paper we introduce a representation of knots and links called a cube diagram. We show that a property of a cube diagram is a link invariant if and only if the property is invariant under two types of cube diagram operations. A knot…
In this article we obtain the classification of the congruences of lines with one-dimensional focal locus. It turns out that one can restrict to study the case of $\mathbb{P}^3$.
We construct a model of the comprehension schema in the logic LP=>.