Publication:
Torus rational fibrations.

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Publication Date
1999
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Elsevier Science B.V. (North-Holland)
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We study rational fibrations where the fibre is an r-dimensional torus and the base is a formal space. We make use of the Eilenberg{Moore Spectral Sequence to prove the Toral Rank Conjecture in some cases.
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C. Allday, S. Halperin, Lie group actions on spaces of finite rank, Quart. J. Math. Oxford 28 (1978)63-76. M. Atiyah, I. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, MA, 1969. Y. Felix, La dichotomie elliptique-hyperbolique en homotopie rationnelle, Asterisque 176 (1989). Y. Felix, D. Tanre, J-C. Thomas, Minimal models and geometry, preprint, 1993. P-P. Grivel, Formes differentielles et suites spectrales, Ann. Inst. Fourier 29 (1979) 17-37. S. Halperin, Finiteness in the minimal models of Sullivan, Trans. Amer. Math. Soc. 230 (1977) 173-199. S. Halperin, Rational brations, minimal models, and fiberings of homogeneous spaces, Trans. Amer.Math. Soc. 244 (1978) 199-224. S. Halperin, Rational homotopy and torus actions, in:Aspects of Topology, In Memory of Hugh Dowker,Lecture Notes Series, vol. 93, 1985, pp. 293-306. J. McCleary, User's Guide to Spectral Sequences,Mathematics Lecture Series, vol. 12, Publish or Perish, Berkeley, CA,1985. D. Tanre, Homotopie Rationnelle: Modeles de Chen,Quillen, Sullivan, Lecture Notes in Maths,vol. 1025,Springer,Berlin, 1983.
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