Simplicial types and polynomial algebras

Gómez, Francisco. "Simplicial types and polynomial algebras." Archivum Mathematicum 038.1 (2002): 27-36. <http://eudml.org/doc/248937>.

@article{Gómez2002,
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].},
author = {Gómez, Francisco},
journal = {Archivum Mathematicum},
keywords = {simplicial complex; algebraic de Rham complex; Sullivan’s de Rham complex; simplicial complex; algebraic de Rham complex; Sullivan's de Rham complex},
language = {eng},
number = {1},
pages = {27-36},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Simplicial types and polynomial algebras},
url = {http://eudml.org/doc/248937},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Gómez, Francisco
TI - Simplicial types and polynomial algebras
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 1
SP - 27
EP - 36
AB - 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].
LA - eng
KW - simplicial complex; algebraic de Rham complex; Sullivan’s de Rham complex; simplicial complex; algebraic de Rham complex; Sullivan's de Rham complex
UR - http://eudml.org/doc/248937
ER -