Related papers: The Tensorial Connections
An important goal in studying the relations between unitary VOAs and conformal nets is to prove the equivalence of their ribbon categories. In this article, we prove this conjecture for many familiar examples. Our main idea is to construct…
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…
The scalar-tensor theory of gravitation has been and still is one of the most widely discussed "alternative theories" to General Relativity (GR). Despite nearly half a century of its age, it continues to attract renewed interests of not…
The work reported here originates in the discovery, four decades ago, of a previously unknown type of self-organizing interaction among oscillating systems -- so-called argumental interactions -- and of "quantized" modes of behavior in…
We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…
A natural connection, determined by a property of its torsion tensor, is defined and it is called the second natural connection on Riemannian $\Pi$-manifold, i.e. the uniqueness of this connection is proved and a necessary and sufficient…
We introduce a notion of a connection on a coherent sheaf on a weighted projective line (in the sense of Geigle and Lenzing). Using a theorem of Huebner and Lenzing we show, under a mild hypothesis, that if one considers coherent sheaves…
These are notes from the lectures I gave at the Oberwolfach seminar `Tensor Triangular Geometry and Interactions' which was held in October 2025. The aim of these notes is to give an introduction to tensor triangular geometry, for both…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
We define a decomposition of link projections whose pieces we call atoroidal graphs. We describe a surgery operation on these graphs and show that all atoroidal graphs can be generated by performing surgery repeatedly on a family of well…
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique…
This paper provides a relationship between a geometric structure of a suspended tree and the number of link components of the associated link diagram.
For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the…
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…
We present a critical analysis of what is called Relational Mechanics, as it has been presented in a book thus entitled, which has been recently reviewed in this journal.
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
The hypothesis of existence of off-site continuums is investigated. Principles of the physical description are formulated. The structure of off-site continuums and opportunities of observation of off-site physical objects from the continuum…
This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use…