Related papers: A note on local rigidity

This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…

We demonstrate quasi-isometric rigidity for the product of a non-uniform rank one lattice and a nilpotent lattice. Specifically, we show that any finitely-generated group quasi-isometric to such a product is, up to finite noise, an…

We introduce the notion of soficity for locally compact groups and list a number of open problems.

In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…

Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).

We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients…

We prove a structure theorem for the isometry group Iso(M, g) of a compact Lorentz manifold, under the assumption that a closed subgroup has exponential growth. We don't assume anything about the identity component of Iso(M, g), so that our…

We prove a global topological rigidity theorem for locally $C^2$-non-discrete subgroups of the group of real analytic diffeomorphisms of the circle.

Let $L$ be a slim, planar, semimodular lattice (slim means that it does not contain an ${\mathsf M}_3$-sublattice). We call the interval $I = [o, i]$ of $L$ \emph{rectangular}, if there are complementary $a, b \in I$ such that $a$ is to the…

We prove some boundary rigidity results for the hemisphere under a lower bound for Ricci curvature. The main result can be viewed as the Ricci version of a conjecture of Min-Oo.

This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.

The aim of this note is to discuss resolution theorems that are useful in the study of semi log canonical varieties.

We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not…

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.

In this paper we study certain groups of bilipschitz maps of the boundary minus a point of a negatively curved space that is an abelian-by-cyclic solvable Lie group, where the extension is given by a matrix whose eigenvalues all lie outside…

A vertex-transitive graph $\mathcal{G}$ is called Local-to-Global rigid if there exists $R>0$ such that every other graph whose balls of radius $R$ are isometric to the balls of radius $R$ in $\mathcal{G}$ is covered by $\mathcal{G}$. An…

Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the case that the corresponding Lie algebra…

We study semi-stable ideal lattices coming from real quadratic number fields. Specifically, we demonstrate infinite families of semi-stable and unstable ideal lattices of trace type, establishing explicit conditions on the canonical basis…

The purpose of this note is to start the systematic analysis of cofinal types of topological groups.

We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.