Morse theory and conjugacy classes of finite subgroups II

TL;DR

This paper constructs examples of hyperbolic and CAT(0) groups with finitely presented subgroups containing infinitely many conjugacy classes of finite-order elements, using Morse theory and handle cancellation techniques.

Contribution

It introduces new methods to produce subgroups with infinitely many conjugacy classes of finite-order elements within hyperbolic and CAT(0) groups.

Findings

Constructed a hyperbolic group with a finitely presented subgroup having infinitely many conjugacy classes of finite-order elements.

Used Morse theory with high-dimensional horizontal cells to analyze subgroup structures.

Applied handle cancellation to generate additional examples of such subgroups.

Abstract

We construct a hyperbolic group with a finitely presented subgroup, which has infinitely many conjugacy classes of finite-order elements. We also use a version of Morse theory with high dimensional horizontal cells and use handle cancellation arguments to produce other examples of subgroups of CAT(0) groups with infinitely many conjugacy classes of finite-order elements.