Finitely presented groups and homotopy of presentations of triangular algebras

TL;DR

This paper constructs triangular algebras with presentations whose fundamental groups can be any finitely presented group, demonstrating the flexibility of algebraic presentations in relation to group theory.

Contribution

It shows that for any finitely presented group, there exists a triangular algebra with presentations having that group as fundamental group, extending previous results.

Findings

Existence of triangular algebras with prescribed fundamental groups

Construction of multiple presentations with different fundamental groups

Extension of prior results to collections of finitely presented groups

Abstract

Given any finitely presented group G we find a triangular algebra such that has two presentations, one with fundamental group G and another with trivial group. Thus proving that given a collection G1,...,Gn of finitely presented groups there exist a triangular algebra A such that all Gi appear as fundamental group of some presentation of A, extending one of the result in arXiv:math/0405127v3 [math.RA]