Quasiconvex Subgroups of F_m x Z^n are Convex

TL;DR

This paper studies quasiconvex subgroups of F_m x Z^n, showing their actions on convex hulls are cocompact and providing a complete description of these subgroups.

Contribution

It introduces a detailed analysis of quasiconvex subgroups in F_m x Z^n and characterizes their geometric actions and structure.

Findings

Action of quasiconvex subgroups on convex hulls is cocompact

Complete classification of quasiconvex subgroups of F_m x Z^n

Provides geometric insights into subgroup structure

Abstract

In this paper we analyze the action of a quasiconvex subgroup of F_m x Z^n on the convex hull of its orbit and we show that this action is cocompact. Further, using our techniques, we obtain complete description of the quasiconvex subgroups of F_m x Z^n.