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

Assem, Ibrahim ^[1] ; Bustamante, Juan Carlos ^[1] ; Castonguay, Diane ^[2] ; Novoa Bustos, Cristian ^[3]
1. [1] Université de Sherbrooke
  
  Université de Sherbrooke
  
  CA.10.05.43027, Canadá
2. [2] Universidade Federal de Goiás
  
  Universidade Federal de Goiás
  
  Brasil
3. [3] Pontifícia Universidade Católica de Goiás
  
  Pontifícia Universidade Católica de Goiás
  
  Brasil
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Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 24, Nº. 1, 2005, págs. 79-87
Idioma: inglés
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Resumen
- 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.