# Simplicial types and polynomial algebras

Archivum Mathematicum (2002)

- Volume: 038, Issue: 1, page 27-36
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topGómez, 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 -

## References

top- Lectures on minimal models, Memoires SMF, Nouvelle Série (1983), 9–10. Zbl0536.55003MR0736299
- Homotopy types and Sullivan’s algebras of 0-forms, Topology 16 (1977), 193–197. MR0440539
- Sullivan’s de Rham complex is definable in terms of its 0-forms, Proc. A.M.S. 57 2 (1976), 337–339. MR0410737
- Commutative Algebra, Benjamin, 1980. Zbl0655.00011MR0266911
- Simplicial complexes and ruled manifolds, Math. Zam. 50 1 (1991), 92–97. MR1140356
- Infinitesimal computations in topology, Publ. I.H.E.S. 47 (1977), 269–331. Zbl0374.57002MR0646078

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.