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1998 | 45 | 1 | 115-135
Tytuł artykułu

Variations on a conjecture of Halperin

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Halperin has conjectured that the Serre spectral sequence of any fibration that has fibre space a certain kind of elliptic space should collapse at the $E_2$-term. In this paper we obtain an equivalent phrasing of this conjecture, in terms of formality relations between base and total spaces in such a fibration (Theorem 3.4). Also, we obtain results on relations between various numerical invariants of the base, total and fibre spaces in these fibrations. Some of our results give weak versions of Halperin's conjecture (Remark 4.4 and Corollary 4.5). We go on to establish some of these weakened forms of the conjecture (Theorem 4.7). In the last section, we discuss extensions of our results and suggest some possibilities for future work.
Słowa kluczowe
Rocznik
Tom
45
Numer
1
Strony
115-135
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115, U.S.A.
Bibliografia
  • [Au] Aubry, M. Homotopy Theory and Models, DMV Seminar 24 (1995) Birkhäuser, Basel.
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  • [Fé-Ha2] Y. Félix and S. Halperin, Rational L-S Category and its Applications, Transactions A. M. S. 273 (1982) 1-37.
  • [Fé-Ha-Le] Félix, Y. S. Halperin and J.-M. Lemaire, The Rational LS Category of Products and of Poincaré Duality Complexes, Topology 37 (1998) 749-756.
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  • [Gr-Mo] P. Griffiths and J. Morgan, Rational Homotopy Theory and Differential Forms, Progress in Mathematics, vol. 15, Birkhäuser, Boston 1983.
  • [Ha1] Halperin, S. Finiteness in the Minimal Models of Sullivan, Transactions A. M. S. 230 (1977) 173-199.
  • [Ha2] Halperin, S. Rational Fibrations, Minimal Models and Fiberings of Homogeneous Spaces, Transactions A. M. S. 244 (1978) 199-223.
  • [Ha3] Halperin, S. Lectures on Minimal Models, Mem. S. M. F. 9/10 (1983).
  • [Ha-St] S. Halperin and J. Stasheff, Obstructions to Homotopy Equivalences, Advances in Math. 32 (1979) 233-279.
  • [He] Hess, K. A Proof of Ganea's Conjecture for Rational Spaces, Topology 30 (1991) 205-214.
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  • [Lu] Lupton, G. Note on a Conjecture of Stephen Halperin, Springer Lecture Notes in Mathematics, vol. 1440, 1990, pp. 148-163.
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  • [Ma] Markl, M. Towards One Conjecture on Collapsing of the Serre Spectral Sequence, Rend. Circ. Mat. Palermo (2) Suppl. 22 (1990) 151-159.
  • [Me] Meier, W. Rational Universal Fibrations and Flag Manifolds, Math. Ann. 258 (1983) 329-340.
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Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv45i1p115bwm
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