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1997 | 73 | 2 | 261-283
Tytuł artykułu

On compact symplectic and Kählerian solvmanifolds which are not completely solvable

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We are interested in the problem of describing compact solvmanifolds admitting symplectic and Kählerian structures. This was first considered in [3, 4] and [7]. These papers used the Hattori theorem concerning the cohomology of solvmanifolds hence the results obtained covered only the completely solvable case}. Our results do not use the assumption of complete solvability. We apply our methods to construct a new example of a compact symplectic non-Kählerian solvmanifold.
Rocznik
Tom
73
Numer
2
Strony
261-283
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-06-07
poprawiono
1996-10-02
Twórcy
  • Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] E. Abbena, An example of an almost Kähler manifold which is not Kählerian, Boll. Un. Mat. Ital. (6) 3-A (1984), 383-392.
  • [2] L. Auslander, An exposition of the structure of solvmanifolds, Bull. Amer. Math. Soc. 79 (1973), 227-285.
  • [3] C. Benson and C. S. Gordon, Kähler and symplectic structures on nilmanifolds, Topology 27 (1988), 513-518.
  • [4] C. Benson and C. S. Gordon, Kähler structures on compact solvmanifolds, Proc. Amer. Math. Soc. 108 (1990), 971-980.
  • [5] L. A. Cordero, M. Fernandez and A. Gray, Symplectic manifolds with no Kähler structure, Topology 25 (1986), 375-380.
  • [6] P. Deligne, P. Griffiths, J. Morgan and D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975), 245-274.
  • [7] M. Fernández, M. de León and M. Saralegui, A six-dimensional compact symplectic solvmanifold without Kähler structures, Osaka J. Math. 33 (1996), 19-35.
  • [8] R. Gompf, Some new symplectic 4-manifolds, Turkish J. Math. 18 (1994), 7-15.
  • [9] S. Halperin, Lectures on Minimal Models, Hermann, 1982.
  • [10] K. Hasegawa, Minimal models of nilmanifolds, Proc. Amer. Math. Soc. 106 (1989), 67-71.
  • [11] A. Hattori, Spectral sequence in the de Rham cohomology of fibre bundles, J. Fac. Sci. Univ. Tokyo Sect. 1 8 (1960), 289-331.
  • [12] K. Hess, Twisted tensor products of DGA's and the Adams-Hilton model for the total space of a fibration, in: London Math. Soc. Lecture Note Ser. 175, Cambridge Univ. Press, 1992, 29-51.
  • [13] D. Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966), 431-449.
  • [14] D. Lehmann, Théorie homotopique des formes différentielles (d'après D. Sullivan), Astérisque 45 (1977).
  • [15] G. Lupton and J. Oprea, Symplectic manifolds and formality, J. Pure Appl. Algebra 91 (1994), 193-207.
  • [16] D. McDuff, Examples of symplectic simply connected manifolds with no Kähler structure, J. Differential Geom. 20 (1984), 267-277.
  • [17] C. McCord and J. Oprea, Rational Lusternik-Schnirelmann category and the Arnold conjecture for nilmanifolds, Topology 32 (1993), 701-717.
  • [18] G. D. Mostow, Factor spaces of solvable groups, Annals of Math. 60 (1954), 1-27.
  • [19] M. Raghunathan, Discrete Subgroups of Lie Groups, Springer, 1972.
  • [20] M. Schlessinger and J. Stasheff, Deformation theory and rational homotopy type, preprint (1992), 44 pp.
  • [21] J.-P. Serre, Homologie singulière des espaces fibrés, Ann. of Math. 54 (1951), 425-505.
  • [22] N. Steenrod, The Topology of Fiber Bundles, Princeton Univ. Press, 1951.
  • [23] D. Tanré, Homotopie Rationnelle: Modèles de Chen, Quillen, Sullivan, Springer, 1983.
  • [24] J.-C. Thomas, Homotopie rationnelle des fibrés de Serre, Université des Sciences et Techniques de Lille I, 1980.
  • [25] J.-C. Thomas, Rational homotopy of Serre fibrations, Ann. Inst. Fourier (Grenoble) 31 (3) (1981), 71-90.
  • [26] E. Vinberg, V. Gorbatsevich and O. Shvartsman, Discrete Subgroups of Lie Groups, Itogi Nauki i Tekhniki. Sovremennye Problemy Matematiki 21 (1988), 5-115 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv73i2p261bwm
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