Related papers: HNN extensions and embedding theorems for groups

We prove that the property of a free group endomorphism being irreducible is a group invariant of the ascending HNN extension it defines. This answers a question posed by Dowdall-Kapovich-Leininger. We further prove that being irreducible…

A subgroup $H$ of a group $G$ is confined if the $G$-orbit of $H$ under conjugation is bounded away from the trivial subgroup in the space $\operatorname{Sub}(G)$ of subgroups of $G$. We prove a commutator lemma for confined subgroups. For…

We develop a theory of polymatroids on Stallings core graphs, which provides a new technique for proving lower bounds on stable invariants of words and subgroups in free groups $F$, and for upper bounds on their probability for mapping,…

We study Hecke algebras of groups acting on trees with respect to geometrically defined subgroups. In particular, we consider Hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and…

We observe that the group of all lifts of elements of Thompson's group $T$ to the real line is finitely presented and contains the additive group $\mathbb{Q}$ of the rational numbers. This gives an explicit realization of the Higman…

In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.

The Baumslag-Solitar group is an example of an HNN extension. Spielberg showed that it has a natural positive cone, and that it is then a quasi-lattice ordered group in the sense of Nica. We give conditions for an HNN extension of a…

In this work, we introduce a hypergraph representation learning framework called Hypergraph Neural Networks (HNN) that jointly learns hyperedge embeddings along with a set of hyperedge-dependent embeddings for each node in the hypergraph.…

We study the Segal-Bargmann transform on the Heisenberg motion groups $\mathbb{H}^n \ltimes K,$ where $\mathbb{H}^n$ is the Heisenberg group and $K$ is a compact subgroup of $U(n)$ such that $(K,\mathbb{H}^n)$ is a Gelfand pair. The Poisson…

Let $1 \le r < n$ be integers. We give a proof that the group $\mathop{\mathrm{Aut}}({X_{n}^{\mathbb{N}}, \sigma_{n}})$ of automorphisms of the one-sided shift on $n$ letters embeds naturally as a subgroup $\mathcal{H}_{n}$ of the outer…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

Stallings remarked that an outer automorphism of a free group may be thought of as a subdivision of a graph followed by a sequence of folds. In this thesis, we prove that automorphisms of fundamental groups of graphs of groups satisfying…

We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and…

The longstanding conjecture of Halin characterizing the existence of normal spanning trees in infinite graphs has been recently proved by Max Pitz [3]. A critical step in the proof involves the construction of dominated torsos, whose…

We prove a Filling Theorem for the Heisenberg Groups $H^{2n+1}$: For a given $k$-cycle $a$ we construct a $(k+1)$-chain $b$ (the filling) with boundary $\partial b=a$ and controlled volume. For this filling $b$ we prove a uniform bound on…

We construct the HNN extension of discrete quantum groups, we study their representation theory and we show that an HNN extension of amenable discrete quantum groups is K-amenable.

Numerous Lie supergroups do not admit superunitary representations except the trivial one, e.g., Heisenberg and orthosymplectic supergroups in mixed signature. To avoid this situation, we introduce in this paper a broader definition of…

For certain HNN extensions including Baumslag-Solitar groups, a treeing is constructed from their certain probability-measure-preserving actions. This is a treeing of a quotient groupoid of the translation groupoid associated with their…

Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI approaches are not applicable. To a large extent,…

We study and compare different Graph Neural Network extensions that increase the expressive power of GNNs beyond the Weisfeiler-Leman test. We focus on (i) GNNs based on higher order WL methods, (ii) GNNs that preprocess small substructures…