Fundamental groups of Peano continua

TL;DR

This paper proves that countable fundamental groups of Peano continua are finitely presented, extending Shelah's theorem using geometric group theory techniques.

Contribution

It extends Shelah's theorem to Peano continua, showing their countable fundamental groups are finitely presented, a new connection between topology and geometric group theory.

Findings

Countable fundamental groups of Peano continua are finitely presented.

The proof employs ideas from geometric group theory.

Extension of Shelah's theorem to a broader class of spaces.

Abstract

Extending a theorem of Shelah we prove that fundamental groups of Peano continua (locally connected and connected metric compact spaces) are finitely presented if they are countable. The proof uses ideas from geometric group theory.