Transactions of the American Mathematical Society

Author(s): Aniceto Murillo
Journal: Trans. Amer. Math. Soc. 359 (2007), 3577-3587.
MSC (2000): Primary 57P10, 55R05, 18G15
Posted: March 7, 2007
Retrieve article in: PDF

Abstract: In this paper we study a generalization of the homology of the Spivak fiber of a

-connected space over any field and deduce consequences concerning Poincaré complexes, Gorenstein spaces and finiteness properties on fibrations.

1.: L. Avramov and S. Halperin, Through the looking glass: A dictionary between rational homotopy theory and local algebra, in Lecture Notes in Math. 1183 (1986), 1-27.MR 0846435 (87k:55015)
2.: L. Avramov, H. Foxby and J. Lescot, Bass series of local ring homomorphisms of finite flat dimension, Trans. Amer. Math. Soc., 335 (1993), 497-523.MR 1068924 (93d:13026)
3.: R. Bott and L. Tu, ``Differential Forms in Algebraic Topology", G.T.M. 82, Springer, 1995.MR 0658304 (83i:57016)
4.: N. Dupont and K. Hess, Twisted tensor models for fibrations, Journal of Pure and Appl. Algebra 91 (1994), 109-120. MR 1255924 (94m:55017)
5.: Y. Félix, S. Halperin and J.C. Thomas, Gorenstein spaces, Advances in Math. 71 (1989), 92-112. MR 0960364 (89k:55019)
6.: Y. Félix, S. Halperin and J.C. Thomas, Differential graded algebras in topology, in ``Handbook of Algebraic Topology", Elsevier, 1995. MR 1361901 (96j:57052)
7.: Y. Félix, S. Halperin and J.C. Thomas, ``Rational Homotopy Theory", G.T.M. , Springer, 2000.MR 1802847 (2002d:55014)
8.: Y. Félix, J.M. Lemaire and J.C. Thomas, L'application d'évaluation, les groupes de Gottlieb duaux et les cellules terminales, Journal of Pure and Appl. Algebra 91 (1994), 143-164. MR 1255927 (94j:55004)
9.: Y. Félix and A. Murillo, Gorenstein graded algebras and the evaluation map, Canadian Math. Bulletin 41(1) (1998), 28-32. MR 1618931 (99c:57069)
10.: T. Goodwillie and M. Weiss, Embeddings from the point of view of immersion theory: Part II, Geom. Topol. 3 (1999), 103-118. MR 1694808 (2000c:57055b)
11.: D. Gottlieb, Poincaré duality and fibrations, Proc. Amer. Math. Soc. 76 (1979), 148-150.MR 0534407 (81a:57017)
12.: H. Gammelin, Gorenstein space with nonzero evaluation map, Trans. Amer. Math. Soc. 351(8) (1999), 3433-3440. MR 1458300 (99m:16015)
13.: K. Hess, Twisted tensor products of DGA's and the Adams-Hilton model for the total space of a fibration. Adams Memorial Symposium on Algebraic Topology, London Math. Soc. Lecture Note Ser. 175, (1992), 29-51.MR 1170569 (94c:55020)
14.: J. Klein, Poincaré duality embeddings and fiberwise homotopy theory, Topology 38(3) (1999), 597-620.MR 1670412 (2000b:57037)
15.: J. Klein, The dualizing spectrum of a topological group, Math. Annalen 319 (2001), 421-456.MR 1819876 (2001m:55037)
16.: A. Murillo, Rational fibrations in differential homological algebra, Trans. Amer. Math. Soc. 332 (1992), 79-91. MR 1079055 (92j:55019)
17.: A. Murillo, On the evaluation map, Trans. Amer. Math. Soc. 339 (1993), 611-622.MR 1112376 (93m:55021)
18.: A. Murillo, The behavior of Ext through a morphism, Journal of Algebra 192 (1997), 477-503. MR 1452675 (98g:13011)
19.: E.H. Spanier, Homology theory of fiber bundles, Proc. Internat. Congr. Math., Cambridge, Mass., 1950, 390-396. MR 0044838 (13:486b)
20.: M. Spivak, Spaces satisfying Poincaré duality, Topology 6 (1967), 77-102.MR 0214071 (35:4923)

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57P10, 55R05, 18G15

Aniceto Murillo
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, AP. 59, 29080 Málaga, Spain
Email: aniceto@agt.cie.uma.es

DOI: 10.1090/S0002-9947-07-04048-2
PII: S 0002-9947(07)04048-2
Keywords: Poincar\'e complex, Gorenstein space, virtual Spivak fiber
Received by editor(s): February 25, 2005
Posted: March 7, 2007
Additional Notes: The author was partially supported by the research grant MTM2004-06262 from the {\em Ministerio de Educación y Ciencia} and by the European Network HPRN-CT-1999-00119.
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS