Related papers: Fractional Fibonacci groups with an odd number of …

We describe the ring of invariants for the finite orthogonal groups in odd dimension and even characteristic acting on the defining representation. We construct a minimal algebra generating set and describe the relations among the…

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…

For a Fano threefold admitting a full exceptional collection of vector bundles of length four we show that all full exceptional collections consist of shifted vector bundles. We prove this via a detailed study of the group generated by…

In this paper we study the regularized analytic torsion of finite volume hyperbolic manifolds. We consider sequences of coverings $X_i$ of a fixed hyperbolic orbifold $X_0$. Our main result is that for certain sequences of coverings and…

For every $n \geq 1$, let $(\mathrm{FW}_n)$ denote the fixed-point property for median graphs of cubical dimension $n$ (or equivalently, for CAT(0) cube complexes of dimension $n$). In this article, we construct explicit examples of groups…

In this paper, we introduce and characterize a class of parabolically extended structures for relatively hyperbolic groups. A characterization of relative quasiconvexity with respect to parabolically extended structures is obtained using…

The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f: N --> M is an…

We develop a notion of groups that act acylindrically and non-elementarily on simplicial trees, which we call acylindrically arboreal groups. We then prove a complete classification of when graph products of groups and the fundamental…

A large class of orbifold quiver gauge theories admits the action of finite Heisenberg groups of the form \prod_i Heis(Z_{q_i} x Z_{q_i}). For an Abelian orbifold generated by \Gamma, the Z_{q_i} shift generator in each Heisenberg group is…

We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group…

We prove that the automorphism group of every infinitely-ended finitely generated group is acylindrically hyperbolic. In particular $\mathrm{Aut}(\mathbb{F}_n)$ is acylindrically hyperbolic for every $n\ge 2$. More generally, if $G$ is a…

We provide an axiomatization for the variety generated by the $n$-periodic l-pregroup $\mathbf{F}_n(\mathbb{Z})$, for every $n \in \mathbb{Z}^+$, as well as for all possible joins of such varieties; the finite joins form an ideal in the…

In this paper we show that the nontrivial fundamental group $\pi_1 SO(3) ={\Bbb Z}_2$ for the group SO(3) of global proper rotations of a four-dimensional Euclidian space (when a spin structure is introduced preliminarily in that space)…

Let $p$ be an odd prime. Let $F/k$ be a cyclic extension of degree $p$ and of characteristic different from $p$. The explicit constructions of the non-abelian $p^{3}$-extensions over $k$, are induced by certain elements in…

The Donald--Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and for the classical Weyl groups (whose rational group…

Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net $\mathcal A$ with central charge $c=8k$ depends on the "gravitational anomaly" $k\pmod 3$. In…

This paper aims to investigate the self-similarity property in finitely-generated torsion-free nilpotent groups. We establish connections between geometric equivalence and self-similarity in these groups. Moreover, we show that any…

We call a group FJ if it satisfies the $K$- and $L$-theoretic Farrell-Jones conjecture with coefficients in $\mathbb Z$. We show that if $G$ is FJ, then the simple Borel conjecture (in dimensions $\ge 5$) holds for every group of the form…

Let $\mathrm{pod}(n)$ denote the number of partitions of $n$ with odd parts distinct, and ${{r}_{k}}(n)$ be the number of representations of $n$ as sum of $k$ squares. We find the following two arithmetic relations: for any integer $n\ge…

Fix $k \geq 2$. For any $N \geq 1$, let $F_k(N)$ denote the cardinality of the largest subset of $\{1,\dots,N\}$ that does not contain $k$ distinct elements whose product is a square. Erd\H{o}s, S\'ark\H{o}zy, and S\'os showed that $F_2(N)…