Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational

ABSTRACT

We prove that the Reidemeister zeta functions of automorphisms of crystallographic groups with diagonal holonomy ℤ₂ are rational. As a result, we obtain that Reidemeister zeta functions of automorphisms of almost-crystallographic groups up to dimension 3 are rational.

KEYWORDS:

• Almost–crystallographic group
• Reidemeister number
• twisted conjugacy
• zeta function

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 20H15