Related papers: A construction of spherical 3-designs

We verify a construction which, for $\Bbb K$ the reals, complex numbers, quaternions, or octonions, builds a spherical $t$-design by placing a spherical $t$-design on each $\Bbb K$-projective or $\Bbb K$-Hopf fiber associated to the points…

We prove that if X is a spherical t-design and s-distance set with $t\geq 2s-3$, then X has the structure of Q-polynomial association scheme of class s. Also, we describe the parameters of the association scheme.

We find a closed formula for the triple integral on spheres in $\mathbb{R}^{2n}\times\mathbb{R}^{2n}\times\mathbb{R}^{2n}$ whose kernel is given by powers of the standard symplectic form. This gives a new proof to the Bernstein--Reznikov…

We construct examples of 3-dimensional compact aspherical Alexandrov spaces without boundary which are not topological manifolds.

This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.

We suggest a geometric visualization of the process of constructing a triangle with prescribed bisectors that makes the existence of such a triangle geometrically evident.

We classify involutions acting on spherical 3-manifolds up to conjugacy. Our geometric approach provides insights into numerous topological properties of these involutions.

This paper is concerned with the use of the stereographic projection to map the points of a design on the sphere in three dimensions onto a two-dimensional stereogram. Details of the projection and its attendant stereogram are given and the…

We construct a new non-desarguesian projective plane from a complex analytic structure. At the same time the construction can be explained in terms of so called Hrushovski's construction. This supports the hypothesis that in general…

A key tool in our earlier work on ends of manifolds high-dimensional manifolds was an ability to embed cobordisms provided by the Quillen Plus Construction into those ends. Here we develop a `spherical modification' trick which provides a…

We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with $m_1 = 3$.

We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an…

Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast,…

Let X be a scroll over a rational surface. We construct a linear system of surfaces in P^3 yielding a birational map from P^3 to X. We apply this construction to the scrolls of Bordiga and Palatini.

On objects of a triangulated category with a stability condition, we construct a topology.

In this paper we give a generalization of injective and projective complexes.

It is shown that there exists a dihedral acute triangulation of the three-dimensional cube. The method of constructing the acute triangulation is described, and symmetries of the triangulation are discussed.

If a (weighted) spherical design is defined as an integration (cubature) rule for a unitarily invariant space P of polynomials (on the sphere), then any unitary image of it is also such a spherical design. It therefore follows that such…

A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.