Work

Twisted conjugacy growth series of virtually abelian groups

Year: 2025

Type: article

Abstract: We initiate the study of the twisted conjugacy growth series of a finitely generated group, the formal power series associated to the twisted conjugacy growth function. Our main result is that, for a virtually abelian group, this series is always an explicitly computable ‐rational function. As a corollary, we obtain a similar result for the relative growth series of a twisted conjugacy class in a virtually abelian group.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70165

Authors: Alex Evetts, Maarten Lathouwers

Institutions: University of Manchester, KU Leuven

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, Heilbronn Institute for Mathematical Research

Award: The Reidemeister spectrum and the R-infinity property for residually nilpotent groups