Related papers: Groups acting on trees with Tits' independence pro…

For a connected Lie group $G$ and an automorphism $T$ of $G$, we consider the action of $T$ on Sub$_G$, the compact space of closed subgroups of $G$ endowed with the Chabauty topology. We study the action of $T$ on Sub$^p_G$, the closure in…

We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…

Many real discrete optimization problems (DOPs) are $NP$-hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special tructure…

We study non-nesting actions on R-trees. We prove that some natural conditions describing how the group is generated, imply that such an action involves an isometric action on an R-tree. This can be applied to permutation groups, linear…

\textsc{Directed Token Sliding} asks, given a directed graph and two sets of pairwise nonadjacent vertices, whether one can reach from one set to the other by repeatedly applying a local operation that exchanges a vertex in the current set…

We develop a unified approach to the classical Hopf Decomposition (also known as the conservative--dissipative decomposition) for actions of locally compact second countable groups. While the decomposition is well understood for free…

The class, denoted by $\mathscr{S}$, of totally disconnected locally compact groups which are non-discrete, compactly generated, and topologically simple contains many compelling examples. In recent years, a general theory for these groups,…

We prove an acylindrical accessibility theorem for finitely generated groups acting on $\mathbf R$-trees. Namely, we show that if $G$ is a freely indecomposable non-cyclic $k$-generated group acting minimally and $M$-acylindrically on an…

We study contraction groups for automorphisms of totally disconnected locally compcat groups using the scale of the automorphism as a tool. The contraction group is shown to be unbounded when the inverse automorphism has non-trivial scale…

In this note we prove the classical decomposition theorems for certain subgroups of the automorphism group of the Bruhat-Tits tree associated to $\mathrm{PGL}_{2}(F)$, where $F$ is a local field. The results can be used to understand the…

In this paper we study CAT(0) groups and their splittings as graphs of groups. For one-ended CAT(0) groups with isolated flats we prove a theorem characterizing exactly when the visual boundary is locally connected. This characterization…

Let p be a real number with 1<p and different from 2. We study Property (T_lp) for a second countable locally compact group G. Property (T_lp) is a weak version of Kazhdan's Property (T), defined in terms of the orthogonal representations…

This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a…

In 2000, Marc Burger and Shahar Mozes introduced universal groups acting on trees. Such groups provide interesting examples of totally disconnected locally compact groups. Intuitively, these are the largest groups for which all local…

We study two actions of the (degree 0) Picard group on the set of the spanning trees of a finite ribbon graph. It is known that these two actions, denoted $\beta_q$ and $\rho_q$ respectively, are independent of the base vertex $q$ if and…

Let $\Gamma$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $\Gamma$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The…

We study non-nesting actions of groups on real trees. We prove some fixed point theorems for such actions under the assumption that groups are Polish and have comeagre conjugacy classes.

We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the \beta-compactification of G (which is a G-space in a natural way), and their minimal closed…

Classical ergodic theory for integer-group actions uses entropy as a complete invariant for isomorphism of IID (independent, identically distributed) processes (a.k.a. product measures). This theory holds for amenable groups as well.…

We prove that a finitely generated pro-$p$ group acting on a pro-$p$ tree $T$ with procyclic edge stabilizers is the fundamental pro-$p$ group of a finite graph of pro-$p$ groups with edge and vertex groups being stabilizers of certain…