Related papers: Asymptotic cones of finitely presented groups

Each graphon $W:\Omega^2\rightarrow[0,1]$ yields an inhomogeneous random graph model $G(n,W)$. We show that $G(n,W)$ is asymptotically almost surely connected if and only if (i) $W$ is a connected graphon and (ii) the measure of elements of…

Let K be the family of graphs on omega_1 without cliques or independent subsets of size omega_1 . We prove that: 1) it is consistent with CH that every G in K has 2^{omega_1} many pairwise non-isomorphic subgraphs, 2) the following…

Let $F\in\mathrm{Diff}(\mathbb{C}^2,0)$ be a germ of a holomorphic diffeomorphism and let $\Gamma$ be an invariant formal curve of $F$. Assume that the restricted diffeomorphism $F|_{\Gamma}$ is either hyperbolic attracting or rationally…

An $(n-1)$-tuple $a = (a(1), \dots, a(n-1))$ consisting of positive integers is said to be asymptotically hollow if there exist infinitely many positive integers $N$ such that the convex hull, $K(a(n))$, in $n$-dimensional Euclidean space…

We study the asymptotic behaviour of the cohomology of subgroups $\Gamma$ of an algebraic group $G$ with coefficients in the various irreducible rational representations of $G$ and raise a conjecture about it. Namely, we expect that the…

If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x…

A result due to M. Gromov states that any two finitely generated groups {\Gamma} and {\Lambda} are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions…

We show that for non-conjugate subgroups $G_1$ and $G_2$ of a finite group $G$ there exists an extension of $G$ (by a finite group) in which the pre-images of $G_1$ and $G_2$ are not isomorphic. This allows us to show that $\mathbb Z$-coset…

Let X be an affine normal variety with a C^*-action having only positive weights. Assume that X_{reg} has a symplectic 2-form w of weight l. We prove that, when l is not zero, the w is a unique symplectic 2-form of weight l up to…

We present sufficient condition for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their representation as a series of spherical harmonics. The family analyzed is a…

Given a finite group $G$, we denote by $L(G)$ the subgroup lattice of $G$ and by ${\rm Isolated}(G)$ the set of isolated subgroups of $G$. In this note, we describe finite groups $G$ such that $|{\rm Isolated}(G)|=|L(G)|-k$, where…

Let H be a closed, noncompact subgroup of a simple Lie group G, such that G/H admits an invariant Lorentz metric. We show that if G = SO(2,n), with n > 2, then the identity component of H is conjugate to the identity component of SO(1,n).…

We investigate a family of groups acting on a regular tree, defined by prescribing the local action almost everywhere. We study lattices in these groups and give examples of compactly generated simple groups of finite asymptotic dimension…

The well-known asymptotic formula for the module of a condenser with one of the plates degenerating to a point is generalized to the case of a condenser of general type. The condensers under consideration consist of n plates, n > 2, and the…

Let S be a distributive {∨, 0}-semilattice. In a previous paper, the second author proved the following result: Suppose that S is a lattice. Let K be a lattice, let $\phi$: Con K $\to$ S be a {∨, 0}-homomorphism. Then $\phi$ is,…

A semigroup is \emph{amiable} if there is exactly one idempotent in each $\mathcal{R}^*$-class and in each $\mathcal{L}^*$-class. A semigroup is \emph{adequate} if it is amiable and if its idempotents commute. We characterize adequate…

Let M be an oriented compact positively curved 4-manifold. Let G be a finite subgroup of the isometry group of $M$. Among others, we prove that there is a universal constant C (cf. Corollary 4.3 for the approximate value of C), such that if…

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement…

It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if $\kappa$ is a cardinal such that $2 \leq \kappa \leq 2^{\aleph_0}$ then the $\kappa$-fold cone has the…

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…