Rational growth in torus bundle groups of odd trace

TL;DR

This paper investigates the rational growth properties of torus bundle groups, extending previous results to a broader class of these groups, and explores their algebraic and geometric characteristics.

Contribution

The paper generalizes the known rational growth results from a subset to all torus bundle groups, broadening understanding of their algebraic structure.

Findings

Certain torus bundle groups have rational growth series

Extension of rational growth results to a larger class of groups

Enhanced understanding of algebraic properties of torus bundle groups

Abstract

A group is said to hae a rational growth with respect to the generating set if the growth series is a rational polynomial. It was shown by Parry that a subset of torus bundle groups exhibits rational growth. We generalize this result to other torus bundle groups.