|
Gorenstein space with nonzero evaluation map
Author(s):
H.
Gammelin
Journal:
Trans. Amer. Math. Soc.
351
(1999),
3433-3440.
MSC (1991):
Primary 55P62
Posted:
March 29, 1999
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let  be a differential graded algebra of finite type, if  is a Gorenstein graded algebra, then so is  . The purpose of this paper is to prove the converse under some mild hypotheses. We deduce a new characterization of Poincaré duality spaces as well as spaces with a nonzero evaluation map.
References:
- 1.
- J. F. Adams and P. J. Hilton, On the chain algebra of a loop space, Comment. Math. Helv. 30 (1956), 305-330. MR 17:1119b
- 2.
- L. Avaramov and S. Halperin, Through the looking glass: A dictionary between rational homotopy theory and local algebra, Algebra, Algebraic Topology and their Interactions, Lecture Notes in Math., vol. 1183, Springer-Verlag, Berlin, 1986. MR 87k:55015
- 3.
- H. Bass, On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8-28. MR 27:3669
- 4.
- D. Eisenbud, Commutative algebra with view toward algebraic geometry, Graduate Texts in Mathematics, 150, Springer-Verlag, 1995. MR 97a:13001
- 5.
- Y. Félix, S. Halperin and J. C. Thomas, Gorenstein spaces, Adv. in Math. 71 (1988), 92-112. MR 89k:55019
- 6.
- -, The homotopy Lie algebra for finite complexes, Inst. Hautes Études Sci. Publ. Math 56 (1982), 179-202. MR 85c:55010
- 7.
- Y. Félix, J.-M. Lemaire and J. C. Thomas, L'application d'évaluation, les groupes de Gottlieb duaux et les cellules terminales, J. Pure and Applied Algebra 91 (1994), 143-164. MR 94j:55004
- 8.
- S. Halperin, Lectures on minimal models, Mém. Soc. Math. France 244 (1978), 199-224. MR 85i:55009
- 9.
- S. Halperin and J. Stasheff, Obstructions to homotopy equivalences, Adv. in Math. 32 (1979), 233-279. MR 80j:55016
- 10.
- H. Matsumura, Commutative algebra, Benjamin, New York, 1970. MR 42:1813
- 11.
- J. C. Moore, Algèbre homologique et homologie des espaces classifants, Séminaire Cartan 1959/1960, exposé 7.
- 12.
- A. Murillo, Rational fibrations in differential homological algebra, Trans. Amer. Math. Soc. 332 (1992), 79-91. MR 92j:55019
- 13.
- -, On the evaluation map, Trans. Amer. Math. Soc. 339 (1993), 611-622. MR 93m:55021
- 14.
- D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1978), 269-331. MR 58:31119
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(1991):
55P62
Retrieve articles in all Journals with MSC
(1991):
55P62
Additional Information:
H.
Gammelin
Affiliation:
Département de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve D'Ascq, France
Email:
gammelin@gat.univ-lille1.fr
DOI:
10.1090/S0002-9947-99-02092-9
PII:
S 0002-9947(99)02092-9
Keywords:
Gorenstein space,
Cohen-Macaulay ring,
Poincar\'e duality space,
evaluation map
Received by editor(s):
December 2, 1996
Posted:
March 29, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
|
Comments: webmaster@ams.org