Fat bundles and formality

• Autorzy: Wojciech Andrzejewski , Aleksy Tralle
• Języki publikacji: EN

Abstrakty

EN

We prove the formality property of total spaces of fat bundles over compact homogeneous spaces. Some rational homotopy obstructions to fatness are obtained.

Słowa kluczowe

EN

fat bundle; formality; symplectic structure

Kategorie tematyczne

• 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
• 55P62: Rational homotopy theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996-1997
• Tom: 65
• Numer: 2
• Strony: 105-118

Daty

wydano

1997

otrzymano

1994-04-26

poprawiono

1995-05-02

poprawiono

1996-07-08

Twórcy

autor

Wojciech Andrzejewski

• Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

autor

Aleksy Tralle

• Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

Bibliografia

• [1] C. Allday and V. Puppe, Cohomology Theory of Transformation Groups, Cambridge Univ. Press, 1993.
• [2] L. Bérard-Bergery, Sur certaines fibrations d'espaces homogènes riemanniennes, Compositio Math. 30 (1975), 43-61.
• [3] P. Deligne, P. Griffiths, J. Morgan and D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975), 245-274.
• [4] A. Dumańska-Małyszko, Z. Stępień and A. Tralle, Generalized symmetric spaces and minimal models, Ann. Polon. Math. 64 (1996), 17-35.
• [5] V. Greub, S. Halperin and R. Vanstone, Connections, Curvature and Cohomology, Academic Press, New York, 1976.
• [6] S. Halperin, Lectures on Minimal Models, Hermann, Paris, 1982.
• [7] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 2, Interscience Publ., New York, 1969.
• [8] D. Lehmann, Théorie homotopique des formes différentielles (d'après D. Sullivan), Astérisque 45 (1977).
• [9] G. Lupton and J. Oprea, Symplectic manifolds and formality, J. Pure Appl. Algebra 91 (1994), 193-207.
• [10] R. Narasimhan and S. Ramanan, Existence of universal connections, Amer. J. Math. 83 (1961), 536-572.
• [11] J.-C. Thomas, Rational homotopy of Serre fibrations, Ann. Inst. Fourier (Grenoble) 31 (3) (1981), 71-90.
• [12] I. Vaisman, Symplectic Geometry and Secondary Characteristic Classes, Birkhäuser, Basel, 1988.
• [13] M. Vigué-Poirrier and D. Sullivan, Cohomology theory of the closed geodesic problem, J. Differential Geom. 11 (1976), 633-644.
• [14] A. Weinstein, Fat bundles and symplectic manifolds, Adv. in Math. 37 (1980), 239-250.
• [15] P. B. Zwart and W. M. Boothby, On compact, homogeneous symplectic manifolds, Ann. Inst. Fourier (Grenoble) 30 (1) (1980), 129-157.