Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The virtual Spivak fiber, duality on fibrations and Gorenstein spaces


Author: Aniceto Murillo
Journal: Trans. Amer. Math. Soc. 359 (2007), 3577-3587
MSC (2000): Primary 57P10, 55R05, 18G15
DOI: https://doi.org/10.1090/S0002-9947-07-04048-2
Published electronically: March 7, 2007
MathSciNet review: 2302507
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study a generalization of the homology of the Spivak fiber of a $ 1$-connected space over any field and deduce consequences concerning Poincaré complexes, Gorenstein spaces and finiteness properties on fibrations.


References [Enhancements On Off] (What's this?)

  • 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$ _A(R,A)$ 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)

Similar Articles

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

Retrieve articles in all journals with MSC (2000): 57P10, 55R05, 18G15


Additional Information

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

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

American Mathematical Society