Regluing graphs of Free Groups

TL;DR

This paper proves that for any finite graph of roses, there exists a regluing that results in a graph with a hyperbolic fundamental group, addressing a question posed by Min.

Contribution

It introduces a method to perform regluings on graphs of roses to achieve hyperbolicity of the fundamental group, providing a positive answer to Min's question.

Findings

Existence of regluings leading to hyperbolic fundamental groups

Construction method for regluings on graphs of roses

Addresses an open question in geometric group theory

Abstract

Answering a question due to Min, we prove that a finite graph of roses admits a regluing such that the resulting graph of roses has hyperbolic fundamental group.