A note on the fundamental group of a one-point extension


  • Ibrahim Assem Université de Sherbrooke.
  • Juan Carlos Bustamante Université de Sherbrooke.
  • Diane Castonguay Universidade Federal de Goiás.
  • Cristian Novoa Bustos Universidade Católica de Goiás.




Fundamental groups, Bound quivers, Presentations of algebras.


In this note, we consider an algebra A which is a one-point extension of another algebra B and we study the morphism of fundamental groups induced by the inclusion of (the bound quiver of ) B into (that of ) A. Our main result says that the cokernel of this morphism is a free group and we prove some consequences from this fact.

Author Biographies

Ibrahim Assem, Université de Sherbrooke.

Département de Mathématiques.

Juan Carlos Bustamante, Université de Sherbrooke.

Département de Mathématiques.

Diane Castonguay, Universidade Federal de Goiás.

Instituto de Informática.

Cristian Novoa Bustos, Universidade Católica de Goiás.

Departameto de Matemática e Física.


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How to Cite

I. Assem, J. C. Bustamante, D. Castonguay, and C. Novoa Bustos, “A note on the fundamental group of a one-point extension”, Proyecciones (Antofagasta, On line), vol. 24, no. 1, pp. 79-87, Apr. 2017.




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