Simplicial types and polynomial algebras

Francisco Gomez

Address. Department of Algebra, Geometry and Topology, University of Malaga, AP 59 29080-Malaga, SPAIN


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.