Related papers: Singular chains and the fundamental group

We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-minimal structures. All results are well-known and an extensive…

We give a simple algebraic description of opetopes in terms of chain complexes, and we show how this description is related to combinatorial descriptions in terms of treelike structures. More generally, we show that the chain complexes…

In anabelian geometry, we consider to what extent the \'{e}tale or tame fundamental groups of schemes reflect geometric properties of the schemes. Although there are many known results (mainly for smooth curves) in this area, general…

As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…

We exhibit a map f between aspherical spaces X and Y such that f induces an isomorphism on homotopy groups but, with natural topologies, X and Y fail to have homeomorphic fundamental groups. Thus the topological fundamental group has the…

This thesis addresses the theory of topological spaces and the foundations of persistence theory. We will discuss chain complexes and the associated simplicial homology groups, as well as their relationship with singular homology theory.…

Let G be a reductive groups over an algebraically closed field k. Let P^{(i)} be associated parabolic subgroups, and X^{(i)}:=T^*G/P^i. The bounded derived categories of coherent sheaves on X^{(i)} are equivalent, but there is no canonical…

Function clones are sets of functions on a fixed domain that are closed under composition and contain the projections. They carry a natural algebraic structure, provided by the laws of composition which hold in them, as well as a natural…

Tree-graded spaces are a generalization of $\mathbb{R}$-trees and play an important role in describing the large-scale geometry of relatively hyperbolic groups. We consider a subclass of tree-graded spaces that we call "disjointly…

Let $G_\Gamma$ be a graph product over a finite simplicial graph $\Gamma$, and let $K_\Gamma$ denote the kernel of the canonical homomorphism from $G_\Gamma$ to the direct product of its vertex groups. It is known that, up to isomorphism,…

The fundamental group of the complement of a plane curve is a very important topological invariant. In particular, it is interesting to find out whether this group is determined by the combinatorics of the curve or not, and whether it is a…

In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type $\tto$ factors arising from countable discrete groups. We give simple criteria for…

Two distinct structures of aggregates of atoms connected by anisotropic bonds with a network configuration are discussed from the viewpoint of a point set topology. A specific topological space connects the two types of topological…

The abundance of data about social relationships allows the human behavior to be analyzed as any other natural phenomenon. Here we focus on balance theory, stating that social actors tend to avoid establishing cycles with an odd number of…

A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…

We compute the sandpile groups of families of planar graphs having a common weak dual by evaluating the indeterminates of the critical ideals of the weak dual at the lengths of the cycles bounding the interior faces. This method allow us to…

Motivated by the hinge structure present in protein chains and other molecular conformations, we study the singularities of certain maps associated to body-and-hinge and panel-and-hinge chains. These are sequentially articulated systems…

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…

We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways…