相关论文: Peripherally specified homomorphs of link groups

We extend the notion of 'homomorphism-homogeneity' to a wider class of kinds of maps than previously studied, and we investigate the relations between the resulting notions of homomorphism-homogeneity, giving several examples. We also give…

Core-periphery structure, the arrangement of a network into a dense core and sparse periphery, is a versatile descriptor of various social, biological, and technological networks. In practice, different core-periphery algorithms are often…

The hyperbolic network models exhibit very fundamental and essential features, like small-worldness, scale-freeness, high-clustering coefficient, and community structure. In this paper, we comprehensively explore the presence of an…

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…

This note is a continuation of the paper [2] (see references). We describe some natural pseudogroup structures on almost complex manifolds of type $m$. A kind of coherency is discussed for the sheaf of almost holomorphic functions.

We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and…

We inductively define layers of colorings of knot and knotted surface diagrams using ternary quasigroups. Homological invariants from such systems of colorings use shorter differentials and of higher degree than the standard homology…

The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost…

It is known that holomorphic Poisson structures are closely related to theories of generalized K\"{a}hler geometry and bi-Hermitian structures. In this article, we introduce quantization of holomorphic Poisson structures which are closely…

Biracks are algebraic structures related to knots and links. We define a new enhancement of the birack counting invariant for oriented classical and virtual knots and links via algebraic structures called birack dynamical cocycles. The new…

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

Relative self-linking and linking "numbers" for pairs of knots in oriented 3-manifolds are defined in terms of intersection invariants of immersed surfaces in 4-manifolds. The resulting concordance invariants generalize the usual…

The knot group is the fundamental group of a knot or link complement. A necessary and sufficient conditions for a group to be realized as the knot group of some link was provided. This result was shown using the closed braid method.…

A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of homogeneity:…

For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic,…

We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…

We define an algebraic setup of homology for hypergraphs, which defaults to simplicial homology in the case of graphs, and study its basic properties. As part of our study we define algebraic spanning trees of hypergraphs, along with…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this correspondence is not a bijection: more than one quiver may be…

In this paper, we develop holomorphic Jacobi structures. Holomorphic Jacobi manifolds are in one-to-one correspondence with certain homogeneous holomorphic Poisson manifolds. Furthermore, holomorphic Poisson manifolds can be looked at as…