E-mail: fgomez@agt.cie.uma.es
Abstract. This paper shows that the simplicial type of a finite simplicial complex K is determined by its algebra A of polynomial functions on the baricentric coordinates with coefficients in any integral domain. The link between K and A is done through certain admissible matrix associated to K in a natural way. This result was obtained for the real numbers by I.V. Savel'ev [5], using methods of real algebraic geometry. D. Kan and E. Miller had shown in [2] that A determines the homotopy type of the polyhedron associated to K and not only its rational homotopy type as it was previously proved by D. Sullivan in [6].
AMSclassification. 58A10, 55U10, 14F40.
Keywords. Simplicial complex, algebraic de Rham complex, Sullivan's de Rham complex.