Related papers: Non-classical generating sets in Fuchsian Schottky…

On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-torsion divisors (and usually exists, but not unique,…

We give a practical method to compute the 2-torsion subgroup of the Jacobian of a non-hyperelliptic curve of genus $3$, $4$ or $5$. The method is based on the correspondence between the 2-torsion subgroup and the theta hyperplanes to the…

In this study, we define a brief description of the hyperbolic and elliptic rotational surfaces using a curve and matrices in 4-dimensional semi Euclidean space. That is, we provide different types of rotational matrices, which are the…

We introduce the concept of a Fock bundle, a smooth principal bundle over a surface equipped with a special kind of adjoint-valued 1-form, as a new tool for studying character varieties of surface groups. Although similar to Higgs bundles,…

In this paper, we present a new approach to the problem of designing hyperbolic signal sets matched to groups by use of Whittaker's proposal in the uniformization of hyperelliptic curves via Fuchsian differential equations (FDEs). This…

Noncommutative geometry provides a framework, via the construction of spectral triples, for the study of the geometry of certain classes of fractals. Many fractals are constructed as natural limits of certain sets with a simpler structure:…

We consider three families of groups: the Bianchi groups SL(2,O) where O is the ring of integers of an imaginary, quadratic field; the groups SL*(2,O) where O is a *-order of a definite, rational quaternion algebra with an orthogonal…

We study the distribution of normal subgroups in non-torsion, regular branch multi-EGS groups and show that the congruence completions of such groups have bounded finite central width. In particular, we show that the profinite completion of…

In this paper we create many examples of hyperbolic groups with subgroups satisfying interesting finiteness properties. We give the first examples of subgroups of hyperbolic groups which are of type $FP_2$ but not finitely presented. We…

Real-valued band structures are foundational to analyzing periodic systems within the Hermitian description and have been experimentally well-established over recent decades. In contrast, non-Hermitian systems exhibit complex band…

We give examples of hyperbolic groups which contain subgroups that are of type $\mathscr{F}_{3}$ but not of type $\mathscr{F}_{4}$. These groups are obtained by Dehn filling starting from a non-uniform lattice in ${\rm PO}(8,1)$ which was…

Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichm\"uller space, right-angled Artin groups, and many other cubical groups. Given such a space $\mathcal X$, we build…

We consider 2-local geometries and other subgroup complexes for sporadic simple groups. For six groups, the fixed point set of a noncentral involution is shown to be equivariantly homotopy equivalent to a standard geometry for the component…

Following the continuing interest in the Urysohn space and, more specifically, the recent problem area of finding and comparing group structures on the Urysohn space we prove that there exists a non-abelian group structure on the Urysohn…

We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus.

We construct new examples of CAT(0) groups containing non finitely presented subgroups that are of type $FP_2$, these CAT(0) groups do not contain copies of $\mathbb{Z}^3$. We also give a construction of groups which are of type $F_n$ but…

In this paper we investigate Uludag's method for constructing new curves whose fundamental groups are central extensions of the fundamental group of the original curve by finite cyclic groups. In the first part, we give some generalizations…

We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Specifically, our examples are extensions of infinite torsion…

We consider lattices generated by finite Abelian groups. We prove that such a lattice is strongly eutactic, which means the normalized minimal vectors of the lattice form a spherical 2-design, if and only if the group is of odd order or if…

In this paper, we initiate the study of nondiagonal finite quasi-quantum groups over finite abelian groups. We mainly study the Nichols algebras in the twisted Yetter-Drinfeld module category $_{\k G}^{\k G}\mathcal{YD}^\Phi$ with $\Phi$ a…