Related papers: Fundamental Groups of Simplicial Complexes

In this paper, we prove that the fundamental group of a simplicial complex is isomorphic to the algebraic fundamental group of its incidence algebra, and we derive some applications.

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

The prime simplicial complex $\Pi(G)$ of a finite group $G$ is composed of all sets of primes $S$ where $G$ has an element of order the product of primes in $S$, with the subsets partially ordered by inclusion. This complex was introduced…

The number of nonisomorphic simplicial complexes with up to $n$ vertices increases super-exponentially with $n$, which makes exhaustive computation of invariants associated with such complexes a daunting task. In this paper we provide a…

The edge group of a simplicial complex is a well-known, combinatorial version of the fundamental group. It is a group associated to a simplicial complex that consists of equivalence classes of edge loops and that is isomorphic to the…

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…

In previous work, we have defined---intrinsically, entirely within the digital setting---a fundamental group for digital images. Here, we show that this group is isomorphic to the edge group of the clique complex of the digital image…

We call a set of positive integers closed under taking unitary divisors a unitary ideal. It can be regarded as a simplicial complex. Moreover, a multiplicative arithmetical function on such a set corresponds to a function on the simplicial…

In this paper we show that a simplicial complex can be determined uniquely up to isomorphism by its barycentric subdivision or comparability graph. At the end, it is summarized several algebraic, combinatorial and topological invariants of…

We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of…

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…

We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $2^k -1$ for some $k$; or (c) a projective special linear…

Two finite groups are said to be isospectral if they have the same sets of element orders. This paper completes the description of finite groups that are isospectral to finite simple groups with disconnected prime graph.

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

A graph is split if there is a partition of its vertex set into a clique and an independent set. The present paper is devoted to the splitness of some graphs related to finite simple groups, namely, prime graphs and solvable graphs, and…

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…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…

Let $G$ be a finite group. In 2024, Cameron introduced two different concepts of independence (namely independence and strong independence) for the subsets of $G$, yielding to the definition of two simplicial complexes whose vertices are…

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…