Iwasawa theory of (directed) Cayley graphs

Abstract

In this article, we prove the Defect Conjecture for Cayley graphs of abelian groups, dihedral groups, and groups of the form $\mathbb{Z}/p\mathbb{Z}⋊\mathbb{Z}/(p-1)\mathbb{Z}$ where $p\ge 3$ is a prime. We also compute the Iwasawa invariants of the Bowen--Franks groups associated with these graphs in several cases.