| Title:
|
Simplicial types and polynomial algebras (English) |
| Author:
|
Gómez, Francisco |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
27-36 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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]. (English) |
| Keyword:
|
simplicial complex |
| Keyword:
|
algebraic de Rham complex |
| Keyword:
|
Sullivan’s de Rham complex |
| MSC:
|
55P62 |
| MSC:
|
55U10 |
| MSC:
|
58A10 |
| idZBL:
|
Zbl 1088.55014 |
| idMR:
|
MR1899565 |
| . |
| Date available:
|
2008-06-06T22:29:41Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107816 |
| . |
| Reference:
|
[1] Halperin, S.: Lectures on minimal models.Memoires SMF, Nouvelle Série (1983), 9–10. Zbl 0536.55003, MR 0736299 |
| Reference:
|
[2] Kan, D. M. and Miller, E. Y.: Homotopy types and Sullivan’s algebras of 0-forms.Topology 16 (1977), 193–197. MR 0440539 |
| Reference:
|
[3] Kan, D. M. and Miller, E. Y.: Sullivan’s de Rham complex is definable in terms of its 0-forms.Proc. A.M.S. 57 2 (1976), 337–339. MR 0410737 |
| Reference:
|
[4] Matsumura, H.: Commutative Algebra.Benjamin, 1980. Zbl 0655.00011, MR 0266911 |
| Reference:
|
[5] Savel’ev, I. V.: Simplicial complexes and ruled manifolds.Math. Zam. 50 1 (1991), 92–97. MR 1140356 |
| Reference:
|
[6] Sullivan, D.: Infinitesimal computations in topology.Publ. I.H.E.S. 47 (1977), 269–331. Zbl 0374.57002, MR 0646078 |
| . |
