
TL;DR
This paper explores the relationship between certain closed subgroups of tree isometries, self-replicating groups, and totally disconnected locally compact groups with positive scale, revealing deep structural connections.
Contribution
It establishes a correspondence between specific subgroups fixing an end of a regular tree and self-replicating groups, linking geometric and algebraic group properties.
Findings
Characterization of subgroups fixing an end of the tree
Connection to self-replicating groups acting on rooted trees
Identification of elements with positive scale in locally compact groups
Abstract
Closed subgroups of the group of isometries of the regular tree that fix an end of the tree and are vertex-transitive are shown to correspond, on one hand, to self-replicating groups acting on rooted trees and, on the other hand, to elements of totally disconnected, locally compact groups having positive scale.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Topology and Set Theory
