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