Related papers: A Fundamental Group for Digital Images

The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms…

We discuss implications of the fundamental plane parameters of clusters of galaxies derived from combined optical and X-ray data of a sample of 78 nearby clusters. In particular, we investigate the dependence of these parameters on the…

The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.

We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…

We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering…

Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates…

We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or…

In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine…

A group morphism is constructed, which can be realized as the induced morphism of fundamental groups from a holomorphic map between compact Kahler manifolds, but can not be realized by a holomorphic map between smooth projective varieties.…

We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.

For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…

In this note we investigate to what extent the fundamental group of a metric space can be described as the inverse limit of its discrete fundamental groups. We show that some mild conditions suffice to imply the existence of an isomorphism…

We present a new general theory of function-based hypergraph transformations on finite families of finite hypergraphs. A function-based hypergraph transformation formalises the action of structurally modifying hypergraphs from a family in a…

Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…

The purpose of this note is to consider in detail the construction of derived functors. The classical construction, such as in Cartan-Eilenberg or Grothendieck, is clarified, and it is shown, at the same time, that everything can be…

In this expository paper we describe an unifying approach for many known entropies in Mathematics. First we recall the notion of semigroup entropy h_S in the category S of normed semigroups and contractive homomorphisms, recalling also its…

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.

We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of…