Related papers: Bohr Density of Simple Linear Group Orbits

We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface…

We show that, for pairs of hyperbolic toral automorphisms on the $2$-torus, the points with dense forward orbits under one map and nondense forward orbits under the other is a dense, uncountable set. The pair of maps can be noncommuting. We…

We introduce and study model-theoretic connected components of rings as an analogue of model-theoretic connected components of definable groups. We develop their basic theory and use them to describe both the definable and classical Bohr…

Let $G$ be an acylindrically hyperbolic group. We prove that if $G$ has no non-trivial finite normal subgroups, then the set of invertible elements is dense in the reduced $C^\ast$-algebra of $G$. The same result is obtained for finite…

Let $\Gamma$ be a non-uniform lattice in $\operatorname{PSL}(2,\mathbb R)$. In this note, we show that there exists a constant $\gamma_0>0$ such that for any $0<\gamma<\gamma_0$, any one-parametrer unipotent subgroup $\{u(t)\}_{t\in\mathbb…

In Lie theory, a dense orbit in the unipotent radical of a parabolic group under the adjoint action is called a Richardson orbit. We define a quiver-graded version of Richardson orbits generalising the classical definition in the case of…

We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…

Let $M$ be a compact complex manifold. The corresponding Teichmuller space $\Teich$ is a space of all complex structures on $M$ up to the action of the group of isotopies. The group $\Gamma$ of connected components of the diffeomorphism…

Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. For maps like multiplication by an integer modulo 1, such sets have full…

In this paper, we prove that a \(p\)-block with abelian defect group is inertial if it covers a \(p\)-block of a normal subgroup of \(p\)-power index having only one irreducible Brauer character orbit.

We show that proper Lie groupoids are locally linearizable. As a consequence, the orbit space of a proper Lie groupoid is a smooth orbispace (a Hausdorff space which locally looks like the quotient of a vector space by a linear compact Lie…

Let $\Aa_t$ be the directed quiver of type $\Aa$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank conditions to define the…

This note provides elementary proofs for necessary density conditions for frames and Riesz sequences in the lattice orbit of a discrete series representation that involve the projective stabiliser of the vector. The presented approach…

We prove that for a Baire-generic Riemannian metric on a closed smooth manifold of dimension greater than or equal 3, the union of stationary geodesic nets that are not closed geodesics forms a dense set. This result confirms a…

A strict quantization of a compact symplectic manifold $S$ on a subset $I\subseteq\R$, containing 0 as an accumulation point, is defined as a continuous field of $C^*$-algebras $\{A_{\hbar}\}_{\hbar\in I}$, with $A_0=C_0(S)$, and a set of…

Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…

The complexity of an action of a reductive algebraic group G on an algebraic variety X is the codimension of a generic B-orbit in X, where B is a Borel subgroup of G. We classify affine homogeneous spaces G/H of complexity one. These…

We investigate several situations where the local homogeneity of a geometric structure on a dense open subset of a manifold implies the local homogeneity everywhere. This results in a strengthening of the conclusions in Gromov's open-dense…

The goal of the article is to provide different explicit quantifications of the non density of simple closed geodesics on hyperbolic surfaces. In particular, we show that within any embedded metric disk on a surface, lies a disk of radius…

The \emph{Bohr compactification} of an arbitrary topological group $G$ is defined as the group compactification $(bG,b)$ with the following universal property: for every continuous homomorphism $h$ from $G$ into a compact group $K$ there is…