Obstructions to the existence of monotone Lagrangian embeddings into cotangent bundles of manifolds fibered over the circle
Annales de l'Institut Fourier, Volume 59 (2009) no. 3, pp. 1135-1175.

We extend the constructions and results of Damian to get topological obstructions to the existence of closed monotone Lagrangian embeddings into the cotangent bundle of a space which is the total space of a fibration over the circle.

On étend des constructions et des résultats obtenus par Damian afin d’obtenir des obstructions topologiques à l’existence de plongements lagrangiens monotones dans le fibré cotangent d’un espace fibré sur le cercle.

DOI: 10.5802/aif.2460
Classification: 57R17, 57R58, 57R70, 53D12
Keywords: Lagrangian embeddings, Floer homology, Novikov homology.
Mot clés : plongements lagrangiens, homologie de Floer, homologie de Novikov
Gadbled, Agnès 1

1 Université Louis Pasteur Institut de recherche de mathématique avancée 7, rue René Descartes 67084 Strasbourg (France)
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Gadbled, Agnès. Obstructions to the existence of monotone Lagrangian embeddings into cotangent bundles of manifolds fibered over the circle. Annales de l'Institut Fourier, Volume 59 (2009) no. 3, pp. 1135-1175. doi : 10.5802/aif.2460. http://archive.numdam.org/articles/10.5802/aif.2460/

[1] Arnolʼd, V. I. The first steps of symplectic topology, Uspekhi Mat. Nauk, Volume 41 (1986) no. 6 (252), p. 3-18, 229 | MR | Zbl

[2] Audin, Michèle Fibrés normaux d’immersions en dimension double, points doubles d’immersions lagrangiennes et plongements totalement réels, Comment. Math. Helv., Volume 63 (1988) no. 4, pp. 593-623 | DOI | MR | Zbl

[3] Biran, Paul Lagrangian non-intersections, Geom. Funct. Anal., Volume 16 (2006) no. 2, pp. 279-326 | DOI | MR | Zbl

[4] Buhovski, Lev Homology of Lagrangian Submanifolds in Cotangent Bundles (arXiv:math/0312265) | Zbl

[5] Damian, Mihai Constraints on exact Lagrangians in cotangent bundles of manifolds fibered over the circle (arXiv:0710.0511, to be published in Comment. Math. Helv.)

[6] Floer, Andreas Morse theory for Lagrangian intersections, J. Differential Geom., Volume 28 (1988) no. 3, pp. 513-547 | MR | Zbl

[7] Floer, Andreas The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math., Volume 41 (1988) no. 6, pp. 775-813 | DOI | MR | Zbl

[8] Fukaya, Kenji; Seidel, Paul; Smith, Ivan Exact Lagrangian submanifolds in simply-connected cotangent bundles, Invent. Math., Volume 172 (2008) no. 1, pp. 1-27 | DOI | MR | Zbl

[9] Hind, Richard Lagrangian spheres in S 2 ×S 2 , Geom. Funct. Anal., Volume 14 (2004) no. 2, pp. 303-318 | DOI | MR | Zbl

[10] Lalonde, François; Sikorav, Jean-Claude Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents, Comment. Math. Helv., Volume 66 (1991) no. 1, pp. 18-33 | DOI | EuDML | MR | Zbl

[11] Latour, François Existence de 1-formes fermées non singulières dans une classe de cohomologie de de Rham, Inst. Hautes Études Sci. Publ. Math. (1994) no. 80, pp. 135-194 | DOI | EuDML | Numdam | MR | Zbl

[12] Lê, Hông Vân; Ono, Kaoru Symplectic fixed points, the Calabi invariant and Novikov homology, Topology, Volume 34 (1995) no. 1, pp. 155-176 | DOI | MR | Zbl

[13] Levitt, Gilbert 1-formes fermées singulières et groupe fondamental, Invent. Math., Volume 88 (1987) no. 3, pp. 635-667 | DOI | EuDML | MR | Zbl

[14] Nadler, David Microlocal branes are constructible sheaves (arXiv:math/0612399) | Zbl

[15] Novikov, S. P. Multivalued functions and functionals. An analogue of the Morse theory, Dokl. Akad. Nauk SSSR, Volume 260 (1981) no. 1, pp. 31-35 | MR | Zbl

[16] Oh, Yong-Geun Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I, Comm. Pure Appl. Math., Volume 46 (1993) no. 7, pp. 949-993 | DOI | MR | Zbl

[17] Oh, Yong-Geun Addendum to: Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I., Comm. Pure Appl. Math., Volume 48 (1995) no. 11, pp. 1299-1302 | DOI | MR | Zbl

[18] Oh, Yong-Geun Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Internat. Math. Res. Notices (1996) no. 7, pp. 305-346 | DOI | MR | Zbl

[19] Pazhitnov, A. V. Surgery on the Novikov complex, K-Theory, Volume 10 (1996) no. 4, pp. 323-412 | DOI | MR | Zbl

[20] Polterovich, Leonid Monotone Lagrange submanifolds of linear spaces and the Maslov class in cotangent bundles, Math. Z., Volume 207 (1991) no. 2, pp. 217-222 | DOI | EuDML | MR | Zbl

[21] Ritter, Alexander F. Novikov-symplectic cohomology and exact Lagrangian embeddings (arXiv:0711.1396) | Zbl

[22] Sikorav, Jean-Claude Homologie de Novikov associée à une classe de cohomologie réelle de degré 1 , Thèse Orsay (1987) (Ph. D. Thesis) | MR

[23] Viterbo, Claude Intersection de sous-variétés lagrangiennes, fonctionnelles d’action et indice des systèmes hamiltoniens, Bull. Soc. Math. France, Volume 115 (1987) no. 3, pp. 361-390 | EuDML | Numdam | MR | Zbl

[24] Viterbo, Claude Functors and computations in Floer homology with applications. I, Geom. Funct. Anal., Volume 9 (1999) no. 5, pp. 985-1033 | DOI | MR | Zbl

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