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].
@article{107816,
author = {Francisco G\'omez},
title = {Simplicial types and polynomial algebras},
journal = {Archivum Mathematicum},
volume = {038},
year = {2002},
pages = {27-36},
zbl = {1088.55014},
mrnumber = {1899565},
language = {en},
url = {http://dml.mathdoc.fr/item/107816}
}
Gómez, Francisco. Simplicial types and polynomial algebras. Archivum Mathematicum, Tome 038 (2002) pp. 27-36. http://gdmltest.u-ga.fr/item/107816/
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