Geodesic
Simplicial types and polynomial algebras
Archivum mathematicum, Tome 38 (2002) no. 1, pp. 27-36
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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].
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].
Classification : 55P62, 55U10, 58A10
Keywords: simplicial complex; algebraic de Rham complex; Sullivan’s de Rham complex 
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}
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Gómez, Francisco. Simplicial types and polynomial algebras. Archivum mathematicum, Tome 38 (2002) no. 1, pp. 27-36. http://geodesic.mathdoc.fr/item/ARM_2002_38_1_a2/

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