Diane Castonguay

A NOTE ON THE FUNDAMENTAL GROUP OF A ONE-POINT EXTENSION

1, pp. 79-87, May 2005.Universidad Cat´olica del NorteAntofagasta - ChileAbstractIn this note, we consider an algebra Awhich is a one-point exten-sion of another algebra Band we study the morphism of fundamentalgroups induced by the inclusion of (the bound quiver of) Binto (thatof) A. Our main result says that the cokernel of this morphism is afree group and we prove some consequences from this fact.Subject classification : 16G20.Keywords and phrases : Fundamental groups, bound quivers, pre-sentations of algebras.

A Polynomial Recognition of Unit Forms

Abstract In this paper we introduce a polynomial algorithm for the recognition of weakly nonnegative unit forms. The algorithm identify hypercritical restrictions testing every 9-point subset of the quadratic form associated graph. With Depth First Search strategy, we use a similar approach for the weakly positive recognition.