Tree Pairs for Algebraic Bieri-Strebel Groups
Lewis Molyneux

TL;DR
This paper revisits a method for representing Algebraic Bieri-Strebel groups using tree pairs and shows that some higher order groups lack such representations, indicating no universal degree bound for these groups.
Contribution
It reintroduces a known tree pair construction method and identifies classes of groups that cannot be represented by tree pairs, expanding understanding of their limitations.
Findings
Certain higher degree groups lack tree pair representations
No maximum polynomial degree guarantees a tree pair representation
Reintroduction of a method for constructing tree pair representations
Abstract
We reintroduce a previously discovered method for constructing tree pair representations for Algebraic Bieri-Strebel groups, as well as demonstrate a class of higher order groups that cannot have a tree pair representation. In doing so, we demonstrate that there is no maximum degree such that for all polynomials of higher degree, the associated Algebraic Bieri Strebel group must have a tree-pair representation.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Algebra and Geometry · Geometric and Algebraic Topology
