arXiv subjects

Roman Gorazd

Publications and source records attributed to Roman Gorazd.

4 recordsLinked to original sources

arXiv2026

Gluing diagrams part 1: A constructive solution for the Higman-Thompson group isomorphism problem

This paper introduces gluing diagrams a combinatorial tool to construct homomorphisms between the shift pseudogroups of directed graphs and thus also their full groups of shifts. We will establish which of these diagrams produce isomorphisms. As an application, using the interpretation of Higman-Thompson groups as full groups of shifts of specific graphs, we will describe a procedure that constructs gluing diagrams that explicitly describe the isomorphisms between Higman-Thompson groups, conjectured by Higman and whose existence was proven by Pardo arXiv:1006.1759.

math.GR↗

arXiv2025

Cocompact unfolding trees

This paper will show when a rooted path tree of a finite directed rooted graph has only finitely many orbits under the action of its undirected automorphism group (i.e. when it is cocompact). This will allow us to specify which trees are almost isomorphic to cocompact trees. We will provide an algorithm that will determine this, thus mostly answering question (1) from arXiv:2212.07205.

math.CO↗

arXiv2025

Embedding Higman-Thompson groups of unfolding trees into the Leavitt path algebras

The isomorphism problem of regular Higman-Thompson groups was solved in arXiv:1006.1759, via embedding it into the Leavitt algebra. In this paper, we will expand these results to embed the Higman-Thompson groups of unfolding trees of directed graphs into the Leavitt path algebra. This embedding allows us to show that any isomorphism of rooted Leavitt path algebras induces an isomorphism between Higman-Thompson groups.

math.RA↗

arXiv2023

Classification of Label-Regular Directed Trees up to Almost Isomorphism

This paper outlines a method to determine whether two label-regular directed trees, are isomorphic and when they are almost isomorphic. The approach involves reinterpreting label-regular directed trees as universal covers of rooted graphs. This allows us associate a unique graph with each isomorphism class of a label-regular directed tree. Additionally, by examining the graph monoid we can verify when two unfolding graphs produce almost isomorphic unfolding trees, thereby classifying unfolding trees up to almost isomorphism.

math.CO↗