Related papers: Fundamental groups of small simplicial complexes

We develop a modification of the Zariski--van Kampen approach for the computation of the fundamental group of a trigonal curve with improper fibers. As an application, we list the deformation families and compute the fundamental groups of…

We describe an algorithm which has enabled us to give a complete list, without repetitions, of all closed oriented irreducible 3-manifolds of complexity up to 9. More interestingly, we have actually been able to give a "name" to each such…

We use differential forms on loop spaces to prove that the fundamental group of certain geometric transformation groups is infinite. Examples include both finite and infinite dimensional Lie groups. The finite dimensional examples are the…

Characterizing face-number-related invariants of a given class of simplicial complexes has been a central topic in combinatorial topology. In this regard, one of the well-known invariants is $g_2$. Let $K$ be a normal $3$-pseudomanifold…

The core group is an invariant of unoriented virtual links. We introduce a peripheral structure for the core group, in which the longitudes are sensitive to orientations. We show that the combination of the core group and its peripheral…

We introduce Riemannian metrics of positive scalar curvature on manifolds with Baas-Sullivan singularities, prove a corresponding homology invariance principle and discuss admissible products. Using this theory we construct positive scalar…

We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.

We investigate simplicial complexes deterministically growing from a single vertex. In the first step, a vertex and an edge connecting it to the primordial vertex are added. The resulting simplicial complex has a 1-dimensional simplex and…

We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves. We show that these complexes are strictly developable, and we equip the resulting Basic Construction with…

The 2-girth of a 2-dimensional simplicial complex $X$ is the minimum size of a non-zero 2-cycle in $H_2(X, \mathbb{Z}/2)$. We consider the maximum possible girth of a complex with $n$ vertices and $m$ 2-faces. If $m = n^{2 + \alpha}$ for…

Finite groups with very few character values are characterized. The following is the main result of this article: a finite non-abelian group has precisely four character values if and only if it is the generalized dihedral group of a…

Brehm and K\"uhnel (1992) constructed three 15-vertex combinatorial 8-manifolds `like the quaternionic projective plane' with symmetry groups $\mathrm{A}_5$, $\mathrm{A}_4$, and $\mathrm{S}_3$, respectively. Gorodkov (2016) proved that…

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such nilpotent Lie algebra $\mathfrak{g}$, we describe the space of complex structures on…

Compact pseudo-Riemannian manifolds that have parallel Weyl tensor without being conformally flat or locally symmetric are known to exist in infinitely many dimensions greater than 4. We prove some general topological properties of such…

We show that for a stratum of projectivized abelian differentials with sufficiently many simple zeroes, the inclusion into the appropriate moduli space of pointed curves induces an injection at the level of orbifold fundamental group,…

Integral simplicial volume is a homotopy invariant of oriented closed connected manifolds, defined as the minimal weighted number of singular simplices needed to represent the fundamental class with integral coefficients. We show that…

We calculate the fundamental groups $\pi=\pi_1(P^2\setminus B)$ for all irreducible plane sextics $B\subset\P^2$ with simple singularities for which $\pi$ is known to admit a dihedral quotient $D_{10}$. All groups found are shown to be…

In the 7-vertex triangulation of the torus, the 14 triangles can be partitioned as $T_{1} \sqcup T_{2}$, such that each $T_{i}$ represents the lines of a copy of the Fano plane $PG(2, \mathbb{F}_{2})$. We generalize this observation by…

We produce examples of pairwise non-diffeomorphic closed irreducible 4-manifolds with non-trivial free abelian fundamental group of rank less than three and small Euler characteristic. These exotic smooth structures become standard after…

In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as a special case. We also study…