Related papers: Parsimonious cones
We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational…
Sphere-bases are constructed for the $\mathbb{Z}_2$ vector space formed by the $k$-dimensional subcomplexes, of $n$-simplex (or $n$-cube), for which every $(k{-}1)$-face is contained in a positive even number of $k$-cells; addition is…
Simplification is one of the fundamental operations used in geoinformation science (GIS) to reduce size or representation complexity of geometric objects. Although different simplification methods can be applied depending on one's purpose,…
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
Motivated by the fact that the medial axis transform is able to encode nearly the complete shape, we propose to use as few medial balls as possible to approximate the original enclosed volume by the boundary surface. We progressively select…
Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connected with magnets that can be used to introduce topics like…
Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…
In this paper, we consider constructibility of simplicial 3-balls. In many cases, examining 1-dimensional subcomplexes of a simplicial 3-ball is efficient to solve the decision problem whether the simplicial 3-ball is constructible or not.…
The Golodness of a simplicial complex is defined algebraically in terms of the Stanley-Reisner ring, and it has been a long-standing problem to find its combinatorial characterization. The tightness of a simplicial complex is a…
We construct a polygonal spiral by arranging a sequence of regular $n$-gons such that each $n$-gon shares a specified side and vertex with the $(n+1)$-gon in the construction. By offering flexibility for determining the size of each $n$-gon…
We determine the symmetrized topological complexity of the circle, using primarily just general topology.
An invariant of orientable 3-manifolds is defined by taking the minimum $n$ such that a given 3-manifold embeds in the connected sum of $n$ copies of $S^2 \times S^2$, and we call this $n$ the embedding number of the 3-manifold. We give…
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…
We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…
We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume…
Given a simplicial complex $X$, we construct a simplicial complex $\Omega X$ that may be regarded as a combinatorial version of the based loop space of a topological space. Our construction explicitly describes the simplices of $\Omega X$…
We present a new model which represents data as a mixture of simplices. Simplices are geometric structures that generalize triangles. We give a simple geometric understanding that allows us to learn a simplicial structure efficiently. Our…
It is shown that any smooth closed orientable manifold of dimension $2k + 1$, $k \geq 2$, admits a smooth polynomially convex embedding into $\mathbb C^{3k}$. This improves by $1$ the previously known lower bound of $3k+1$ on the possible…
A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…