Related papers: A note on local rigidity
The paper is a short survey of recent developments in the area of first order descriptions of linear groups. It is aimed to illuminate the known results and to pose the new problems relevant to logical characterizations of Chevalley groups…
A main goal in lattice theory is the construction of dense lattices. Most of the remarkable dense lattices in small dimensions have an additional symmetry, they are modular, i.e. similar to their dual lattice. Extremal lattices are densest…
We prove a super-rigidity result for algebraic representations over complete fields of irreducible lattices in product of groups and lattices with dense commensurator groups. We derive some criteria for non-linearity of such groups.
This paper is about the rigidity of compact group actions in the Poisson context. The main resut is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of…
The purpose of this note is to give a survey on recent progress on characteristic classes of flat bundles, and how they behave in a family.
We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…
New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…
Let $\Gamma \stackrel{i}{\hookrightarrow} L$ be a lattice in the real simple Lie group $L$. If $L$ is of rank at least 2 (respectively locally isomorphic to $Sp(n,1)$) any unbounded morphism $\rho: \Gamma \longrightarrow G$ into a simple…
Let $G$ be a semisimple algebraic group. We develop a machinery for manipulation and manufacture of well-rounded families $\left\{ \mathcal{B}_{T}\right\} _{T>0}\subset G$ as they were defined in a work by A. Gorodnik and A. Nevo. The…
We survey rigidity results for groups acting on the circle in various settings, from local to global and $C^0$ to smooth. Our primary focus is on actions of surface groups, with the aim of introducing the reader to recent developments and…
First we explain the concept of local deformation over a 'parameter' algebra P, in particular the notion of a P-lattice in a Lie group. Purpose of this article is to define the spaces of automorphic resp. cusp forms on the upper half plane…
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature $|\operatorname{sec}|\leq 1$. Moreover, we show that the set of geometric models is compact in the…
We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of nonlinearities.…
In [A. Stolz and A. Thom, On the lattice of normal subgroups in ultraproducts of compact simple groups, PLMS 108(1), 2014] it was stated that the lattice of normal subgroups of an ultraproduct of finite simple groups is always linearly…
A novel structure-preserving algorithm for general relativity in vacuum is derived from a lattice gauge theoretic discretization of the tetradic Palatini action. The resulting model of discrete gravity is demonstrated to preserve local…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
We consider the lattice of coarse structures on a set $X$ and study metrizable, locally finite and cellular coarse structures on $X$ from the lattice point of view.
This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by W.Schmid in [Sch]. A corresponding problem in the compact group setting was solved by…
In this article we prove that the co-compactness of the arithmetic lattices in a connected semisimple real Lie group is preserved if the lattices under consideration are representation equivalent. This is in the spirit of the question posed…