Work

Finitely presented groups with transcendental spectral radius

Year: 2026

Type: article

Abstract: We provide examples of groups with transcendental spectral radius. (1) We first construct finitely presented examples, using links between decidability of the word problem and semi-computability of the spectral radius. This argument extends to the exponential growth rate and the asymptotic entropy. (2) We also construct a finitely generated example with decidable word problem, using classical small-cancellation theory. Along the way, we prove that C'\bigl(\frac{1}{6}\bigr) groups satisfy the rapid decay property and deduce some properties on their spectral radii of independent interest.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/1014

Authors: Corentin Bodart, Denis Osin

Institutions: University of Luxembourg, Vanderbilt University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: G5599649393