Related papers: Single conjugacy classes of isometries in orthogon…

Let $\Omega \subset \mathbb{C}^n$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $\Omega$ to be Reinhardt, complete Reinhardt, circular or Hartogs in terms of the orthogonality…

A prime geodesic theorem for singular geodesics in a locally symmetric space is proved. As an application, an asymptotic formula for units in number fields is given.

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

Let T be a rooted tree and Iso(T) be the group of isometries of T. Using model-theoretic tools we study closed subgroups G of Iso(T) with respect to the number of conjugacy classes of Iso(T) having representatives in G.

Asymptotic Schur orthogonality relations are for irreducible unitary representations of locally compact groups that need not be discrete series, where $L^2$ pairing of matrix coefficients with respect to Haar measure is replaced by a limit…

We introduce bounded cohomology for (pairs of) groupoids and develop homological algebra to deal with it. We generalise results of Ivanov, Frigerio and Pagliantini to this setting and show that (under topological conditions) the bounded…

A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two fundamental groups of simple surface amalgams act properly…

Let k be a field not of characteristic two and L be a set of almost all rational primes invertible in k. Suppose we have a variety X/k and strictly compatible system {M_ell -> X : ell in L} of constructible F_ell-sheaves. If the system is…

We show that the metric of nonpositively curved graph manifolds is determined by its geodesic flow. More precisely we show that if the geodesic flows of two nonpositively curved graph manifolds are $C^0$ conjugate then the spaces are…

We consider finite groups having a conjugacy class that is the difference of two normal subgroups. That is, suppose $G$ is a group and $M$ and $N$ are normal subgroups so that $N < M$, and suppose that there is an element $g \in G$ so that…

A method for implementing non-Abelian duality on string backgrounds is given. It is shown that a direct generalisation of the familiar Abelian duality induces an extra local symmetry in the gauge invariant theory. The non-Abelian isometry…

We establish that standard arithmetic subgroups of a special orthogonal group ${\rm SO}(1,n)$ are conjugacy separable. As an application we deduce this property for unit groups of certain integer group rings. We also prove that finite…

The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…

Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper, we give a nearly complete classification of such groups for…

Let $G$ be a compact, connected simple Lie group and $\mathfrak{g}$ its Lie algebra. It is known that if $\mu $ is any $G$-invariant measure supported on an adjoint orbit in $\mathfrak{g}$, then for each integer $k$, the $k$% -fold…

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…

Any nontrivial homomorphism from the mapping class group of an orientable surface of genus $g\geq 3$ to $\GL(2g,\C)$ is conjugate to the standard symplectic representation. It is also shown that the mapping class group has no faithful…

For $G$ a finite group, let $\kappa(G)$ be the probability that $\sigma,\tau\in G$ are conjugate, when $\sigma$ and $\tau$ are chosen independently and uniformly at random. In this paper, we extend the methods of Blackburn et al [2012] to…

Let $G$ be a group. Two elements $x,y \in G$ are said to be in the same $z$-class if their centralizers in $G$ are conjugate within $G$. Consider $\mathbb F$ a perfect field of characteristic $\neq 2$, which has a non-trivial Galois…

We compute the full isometry group of any left invariant metric on a simply connected, non-unimodular Lie group of dimension three. As an application, we determine the index of symmetry of such metrics and prove that the singularities of…