Related papers: Open Condensed Subgroups and Mackey's Formula

In this note, we lay the groundwork for a new approach to the problem of group-signature classification of group actions on closed Riemann surfaces. This new approach first focuses on analyzing the low level arithmetic conditions on…

The paper studies weak Paley-Wiener properties for group extensions by use of Mackey's theory. The main theorem establishes sufficient conditions on the dual action to ensure that the group has the weak Paley-Wiener property. The theorem…

We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…

We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.

We give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers. This gives further insight into the structure lattices of branch groups introduced by the second author.…

We prove that certain coinduced actions for an inclusion of finitely generated commensurated subgroups with relative one end are continuous cocycle superrigid actions. We also show the necessity for the relative end assumption.

A collection C of subgroups of a finite group G can give rise to three different standard formulas for the cohomology of G in terms of either: the subgroups in C; or their centralizers; or their normalizers. We give a short but systematic…

We develop a theory of convex cocompact subgroups of the mapping class group MCG of a closed, oriented surface S of genus at least 2, in terms of the action on Teichmuller space. Given a subgroup G of MCG defining an extension L_G: 1-->…

Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…

The celebrated Stallings' decomposition theorem states that the splitting of a finite index subgroup $H$ of a finitely generated group $G$ as an amalgamated free product or an HNN-extension over a finite group implies the same for $G$. We…

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative…

First let $G$ be a completely solvable Lie group. We recall the proof of the following result: Any closed subgroup of $G$ possesses a unique syndetic hull in $G$. As a consequence we conclude that any uniform subgroup $\Gamma$ of $G$ is…

A conjecture in [Ish20] states that for a finite subgroup $G$ of $GL(2; \mathbb{C})$, a resolution $Y$ of $\mathbb{C}^2/G$ is isomorphic to a moduli space $\mathcal{M}_{\theta}$ of $G$-constellations for some generic stability parameter…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called (1) $\mathcal C$-$closed$ if $X$ is closed in every topological semigroup $Y\in\mathcal C$ containing $X$ as a discrete subsemigroup, (2) $ideally$ $\mathcal…

Several results in functional analysis are extended to the setting of $L^0$-modules, where $L^0$ denotes the ring of all measurable functions $x\colon \Omega\to \mathbb{R}$. The focus is on results involving compactness. To this end, a…

In this paper we define the notions of normal subcrossed module and quotient crossed module within groups with operations; and using the equivalence of crossed modules over groups with operations and internal groupoids we prove how…

Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal…

Let G be any locally compact, unimodular, metrizable group. The main result of this paper, roughly stated, is that if F<G is any finitely generated free group and \Gamma < G any lattice, then up to a small perturbation and passing to a…

P-E. Caprace and N. Monod isolate the class $\mathscr{X}$ of locally compact groups for which relatively amenable closed subgroups are amenable. It is unknown if $\mathscr{X}$ is closed under group extension. In this note, we exhibit a…

We provide an elementary proof that subgroups of free groups are free via group actions.