Related papers: A Fundamental Group for Digital Images

The main purpose of this paper is to provide a description of the fundamental group of a symplectic manifold in terms of Floer theoretic objects. As an application, we show that when counted with a suitable notion of multiplicity, non…

We define the fundamental group of a Hopf algebra over a field. For this purpose we first consider gradings of Hopf algebras and Galois coverings. The latter are given by linear categories with new additional structure which we call Hopf…

We introduce and analyse a general notion of fundamental group for noncommutative spaces, described by differential graded algebras. For this we consider connections on finitely generated projective bimodules over differential graded…

Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…

We introduce three generalizations of homotopy equivalence in digital images, to allow us to express whether a finite and an infinite digital image are similar with respect to homotopy. We show that these three generalizations are not…

This paper introduces a notion of fundamental group appropriate for laminations.

Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…

We define the notion of fundamental group of an algebraic stack, prove a comparison theorem between the fundamental group of a stack over the complex numbers and that of the associated analytic orbifold, show that this notion coincides with…

A. Rosenfeld introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images,…

We show that a large class of formal groups can be realised functorially by even periodic ring spectra. The main advance is in the construction of morphisms, not of objects.

In this paper, we design two fundamental differential operators for the derivation of rotation differential invariants of images. Each differential invariant obtained by using the new method can be expressed as a homogeneous polynomial of…

For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain…

We extend the definition of fundamental group scheme to non reduced schemes over any connected Dedekind scheme. Then we compare the fundamental group scheme of an affine scheme with that of its reduced part.

The Fundamental Morphism Theorem is a categorical version of the First Noether Isomorphism Theorem for categories that do not have kernels or cokernels. We consider two categories of graphs. Both categories will admit graphs with multiple…

It is well-known that for certain local connectivity assumptions the fundamental groupoid of a topological space can be equipped with a topology making it a topological groupoid. In other words, the fundamental groupoid functor can be…

Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…

We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…

We construct a fundamental region for the action on the $2d+1$-dimensional affine space of some free, discrete, properly discontinuous groups of affine transformations preserving a quadratic form of signature $(d+1, d)$, where $d$ is any…

Morse theory relates algebraic topology invariants and the dynamics of the gradient flow of a Morse function, allowing to derive information about one out of the other. In the case of the homology, the construction extends to much more…