Related papers: Non-stable groups

Let $\Gamma$ be a simplicial, finite, connected graph such that $\Gamma$ does not decompose as a nontrivial join. We prove that two notions of strong quasiconvexity and stability are equivalent in the right-angled Artin group $A_\Gamma$…

We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with…

We consider perturbations of CR structures which preserve the complex tangent bundle. For a compact generic CR manifold its concavity properties and hence the finiteness of some $\overline\partial_b$-cohomology groups are also preserved by…

We prove some finiteness results for discrete isometry groups $\Gamma$ of uniformly packed CAT$(0)$-spaces $X$ with uniformly bounded codiameter (up to group isomorphism), and for CAT$(0)$-orbispaces $M = \Gamma \backslash X$ (up to…

Wahl recently proved that the homology of the non-orientable mapping class group stabilizes as the genus increases. In this short note we analyse the situation where the underlying non-orientable surfaces have marked points.

We study the stable norm on the first homology of a closed, non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm…

A graph $\Gamma$ is said to be stable if for the direct product $\Gamma\times\mathbf{K}_2$, ${\rm Aut}(\Gamma \times \mathbf{K}_2)$ is isomorphic to ${\rm Aut}(\Gamma) \times \mathbb{Z}_2$; otherwise, it is called unstable. An unstable…

For any smooth compact manifold $W$ of dimension at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of $k$ points or $k$ embedded disks (up to permutation) satisfy homology stability. The same…

Let $\Gamma$ be an irreducible lattice in a semisimple Lie group of real rank at least $2$. Suppose that $\Gamma$ has property (T;FD), that is, its finite dimensional representations have a uniform spectral gap. We show that if $\Gamma$ is…

We consider the inverse problem of determining the metric-measure structure of collapsing manifolds from local measurements of spectral data. In the part I of the paper, we proved the uniqueness of the inverse problem and a continuity…

Consider $\operatorname{Sym}(n)$, endowed with the normalized Hamming metric $d_n$. A finitely-generated group $\Gamma$ is \emph{P-stable} if every almost homomorphism $\rho_{n_k}\colon \Gamma\rightarrow\operatorname{Sym}(n_k)$ (i.e., for…

Non-commutative geometries have been proposed as an approach to quantum gravity and have led to the construction of non-commutative black holes, whose interior singularities are purportedly eliminated due to quantum effects. Here we find…

We consider sequences of finitely generated discrete subgroups Gamma_i=rho_i(Gamma) of a rank 1 Lie group G, where the representations rho_i are not necessarily faithful. We show that, for algebraically convergent sequences (Gamma_i),…

Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants,…

The homology groups of many natural sequences of groups $\{G_n\}_{n=1}^{\infty}$ (e.g. general linear groups, mapping class groups, etc.) stabilize as $n \rightarrow \infty$. Indeed, there is a well-known machine for proving such results…

The classification of compact homogeneous spaces of the form $M=G/K$, where $G$ is a non-simple Lie group, such that the standard metric is Einstein is still open. The only known examples are $4$ infinite families and $3$ isolated spaces…

We prove a result on equivariant deformations of flat bundles, and as a corollary, we obtain two ``splitting in a finite cover'' theorems for isometric group actions on Riemannian manifolds with infinite fundamental groups, where the…

Homological stability for unordered configuration spaces of connected manifolds was discovered by Th. Church and extended by O. Randal-Williams and B. Knudsen: $H_i(C_k(M);\mathbb{Q})$ is constant for $k\geq f(i)$. We characterize the…

We present examples of geometrically finite manifolds with pinched negative curvature, whose geodesic flow has infinite non-ergodic Bowen-Margulis measure and whose Poincar\'e series converges at the critical exponent $\delta_\Gamma$. We…

The groups $\Gamma_{n,s}$ are defined in terms of homotopy equivalences of certain graphs, and are natural generalisations of $\mbox{Out}(F_n)$ and $\mbox{Aut}(F_n)$. They have appeared frequently in the study of free group automorphisms,…