Eilenberg-Moore models for fibrations
HTML articles powered by AMS MathViewer
- by J.-C. Thomas PDF
- Trans. Amer. Math. Soc. 274 (1982), 203-225 Request permission
Abstract:
E. M. model is a new invariant in rational homotopy theory which gives us both a Künneth object and a Tate-Josefiak resolution. With the E. M. model, we study relations between formality of base, total space and fibre of a Serre fibration, obstructions to ${\mathbf {k}}$-realizability of a cohomology equivalence between two continuous maps and formalizable maps.References
-
A. K. Bousfield and W. K. A. M. Gugenheim, On the P. L. de Rham theory and rational homotopy type, Mem. Amer. Math. Soc. No. 179 (1976).
- Samuel Eilenberg and John C. Moore, Homology and fibrations. I. Coalgebras, cotensor product and its derived functors, Comment. Math. Helv. 40 (1966), 199–236. MR 203730, DOI 10.1007/BF02564371 Y. Felix, Dénombrement des types de $K$-homotopie-Théorie de la déformation, Nouveaux Mém. Soc. Math. France 3 (1980).
- Yves Félix and Daniel Tanré, Sur la formalité des applications, Publ. U.E.R. Math. Pures Appl. IRMA 3 (1981), no. 2, exp. no. 1, 45 (French). MR 618112
- V. K. A. M. Gugenheim and J. Peter May, On the theory and applications of differential torsion products, Memoirs of the American Mathematical Society, No. 142, American Mathematical Society, Providence, R.I., 1974. MR 0394720
- Stephen Halperin, Rational fibrations, minimal models, and fibrings of homogeneous spaces, Trans. Amer. Math. Soc. 244 (1978), 199–224. MR 515558, DOI 10.1090/S0002-9947-1978-0515558-4 —, Lectures on minimal models, Preprint III, Univ. Sci. Tech. de Lille, 1977.
- Stephen Halperin and James Stasheff, Obstructions to homotopy equivalences, Adv. in Math. 32 (1979), no. 3, 233–279. MR 539532, DOI 10.1016/0001-8708(79)90043-4
- J.-M. Lemaire, “Autopsie d’un meurtre” dans l’homologie d’une algèbre de chaînes, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 1, 93–100 (French, with English summary). MR 500930
- Jean-Michel Lemaire and François Sigrist, Sur les invariants d’homotopie rationnelle liés à la L. S. catégorie, Comment. Math. Helv. 56 (1981), no. 1, 103–122 (French). MR 615618, DOI 10.1007/BF02566201 J. C. Moore, Algébre homologique et homologie des espaces classifiants, Sém. Cartan E. N. S. 59/60 exposé 7. J. D. Stasheff and M. Schlessinger, Deformation theory and rational homotopy type, (preprint).
- Dennis Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269–331 (1978). MR 646078
- J.-C. Thomas, Homotopie rationnelle des fibrés de Serre, Publ. U.E.R. Math. Pures Appl. IRMA 2 (1980), no. 3, exp. no. 4, 27 (English, with French summary). MR 618095
- Micheline Vigué-Poirrier, Réalisation de morphismes donnés en cohomologie et suite spectrale d’Eilenberg-Moore, Trans. Amer. Math. Soc. 265 (1981), no. 2, 447–484 (French). MR 610959, DOI 10.1090/S0002-9947-1981-0610959-8
- Micheline Vigué-Poirrier, Formalité d’une application continue, C. R. Acad. Sci. Paris Sér. A-B 289 (1979), no. 16, A809–A812 (French, with English summary). MR 558804
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 274 (1982), 203-225
- MSC: Primary 55P62; Secondary 55R20
- DOI: https://doi.org/10.1090/S0002-9947-1982-0670928-X
- MathSciNet review: 670928