. Cela-implique-que, est nulle (encore une application de 4.6, mais cette fois-ci pour le groupe ? 1 (F )) Comme l'homologie de Novikov dans les degrés extrémaux est toujours nulle, on obtient que H * (F ; v 2 ) = 0. En particulier ?(F ) = 0, donc F est soit un tore, soit une bouteille de Klein. Mais l'appliquation (v 2 , v 3 )| ? 1 (F ) définit unépimorphismeunépimorphisme de ? 1 (F ) sur Z 2

?. M. Damian, On the homotopy of finite $ {CW}$-complexes with polycyclic fundamental group, Transactions of the American Mathematical Society, vol.361, issue.04, pp.1791-1809, 2009.
DOI : 10.1090/S0002-9947-08-04632-1

?. M. Damian, Constraints on exact Lagrangians in cotangent bundles of manifolds fibered over the circle, Commentarii Mathematici Helvetici, vol.84, pp.705-746, 2009.
DOI : 10.4171/CMH/178

?. M. Damian, Floer homology on the universal cover, a proof of Audin???s conjecture and other constraints on Lagrangian submanifolds, Commentarii Mathematici Helvetici
DOI : 10.4171/CMH/259

?. M. Damian, Floer???Novikov homology and applications to Lagrangian submanifolds, Mathematische Zeitschrift, vol.9, issue.5
DOI : 10.1007/s00209-010-0838-7

P. Arnoux and G. Levitt, Sur l'unique ergodicit??? des 1-formes ferm???es singuli???res, Inventiones Mathematicae, vol.115, issue.1, pp.141-156, 1986.
DOI : 10.1007/BF01388736

M. Audin, Fibr??s normaux d???immersions en dimension double, points doubles d???immersions lagrangiennes et plongements totalement r??els, Commentarii Mathematici Helvetici, vol.63, issue.1, pp.593-623, 1988.
DOI : 10.1007/BF02566781
URL : http://www.digizeitschriften.de/download/PPN358147735_0063/PPN358147735_0063___log35.pdf

M. Audin, F. Lalonde, and L. Polterovich, Symplectic rigidity : Lagrangian submanifolds, Holomorphic Curves in, Progress in Mathematics 117, 1994.

J. Barraud and O. Cornea, Quantization of the Serre spectral sequence, Journal of Symplectic Geometry, vol.5, issue.3, pp.249-280, 2007.
DOI : 10.4310/JSG.2007.v5.n3.a1

R. Bieri, W. Neumann, and R. Strebel, A geometric invariant of discrete groups, Inventiones Mathematicae, vol.9, issue.3, pp.451-477, 1987.
DOI : 10.1007/BF01389175

R. Bieri and B. Renz, Valuations on free resolutions and higher geometric invariants of groups, Commentarii Mathematici Helvetici, vol.63, issue.1, pp.464-497, 1998.
DOI : 10.1007/BF02566775

P. Biran, Lagrangian non-intersections, GAFA Geometric And Functional Analysis, vol.16, issue.2, pp.279-326, 2006.
DOI : 10.1007/s00039-006-0560-0

P. Biran and K. Cieliebak, Symplectic topology on subcritical manifolds, Commentarii Mathematici Helvetici, vol.76, issue.4, pp.712-753, 2001.
DOI : 10.1007/s00014-001-8326-7

P. Biran and O. Cornea, Quantum Structures for Lagrangian submanifolds, 2008.

P. Biran and O. Cornea, Rigidity and uniruling for Lagrangian submanifolds, Geometry & Topology, vol.13, issue.5, 2008.
DOI : 10.2140/gt.2009.13.2881

L. Buhovsky, Homology of Lagrangian submanifolds in cotangent bundles, Israel Journal of Mathematics, vol.100, issue.1, pp.181-187, 2004.
DOI : 10.1007/BF02803498

L. Buhovsky, THE MASLOV CLASS OF LAGRANGIAN TORI AND QUANTUM PRODUCTS IN FLOER COHOMOLOGY, Journal of Topology and Analysis, vol.02, issue.01, pp.55-75, 2010.
DOI : 10.1142/S1793525310000240

R. Chiang, New Lagrangian submanifolds of CP n, Int. Math. Res. Not, vol.45, pp.2437-2441, 2004.

M. Damian, Formes ferm??es non singuli??res et propri??t??s de finitude des groupes, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.33, issue.3, pp.301-320, 2000.
DOI : 10.1016/S0012-9593(00)00112-9

M. Damian, On the homotopy of finite $ {CW}$-complexes with polycyclic fundamental group, Transactions of the American Mathematical Society, vol.361, issue.04, pp.1791-1809, 2009.
DOI : 10.1090/S0002-9947-08-04632-1

M. Damian, Constraints on exact Lagrangians in cotangent bundles of manifolds fibered over the circle, Commentarii Mathematici Helvetici, vol.84, pp.705-746, 2009.
DOI : 10.4171/CMH/178

M. Damian, Floer homology on the universal cover, a proof of Audin???s conjecture and other constraints on Lagrangian submanifolds, Commentarii Mathematici Helvetici
DOI : 10.4171/CMH/259

M. Damian, Floer???Novikov homology and applications to Lagrangian submanifolds, Mathematische Zeitschrift, vol.9, issue.5
DOI : 10.1007/s00209-010-0838-7

D. Mc and . Duff, Symplectic manifolds with contact type boundaries, Invent. Math, vol.103, issue.3, pp.651-671, 1991.

Y. Eliashberg, On symplectic manifolds with some contact properties, Journal of Differential Geometry, vol.33, issue.1, pp.233-238, 1991.
DOI : 10.4310/jdg/1214446036

Y. Eliashberg and L. Polterovich, Local Lagrangian 2-Knots are Trivial, The Annals of Mathematics, vol.144, issue.1, pp.61-76, 1996.
DOI : 10.2307/2118583

D. Epstein, Curves on 2-manifolds and isotopies, Acta Mathematica, vol.115, issue.0, pp.83-107, 1966.
DOI : 10.1007/BF02392203

A. Floer, Morse theory for Lagrangian intersections, Journal of Differential Geometry, vol.28, issue.3, pp.513-547, 1988.
DOI : 10.4310/jdg/1214442477

A. Floer, The unregularized gradient flow of the symplectic action, Communications on Pure and Applied Mathematics, vol.108, issue.6, pp.775-813, 1988.
DOI : 10.1002/cpa.3160410603

A. Floer, Symplectic fixed points and holomorphic spheres, Communications In Mathematical Physics, vol.17, issue.106, pp.575-611, 1989.
DOI : 10.1007/BF01260388

A. Floer, Witten's complex and infinite-dimensional Morse theory, Journal of Differential Geometry, vol.30, issue.1, pp.207-221, 1989.
DOI : 10.4310/jdg/1214443291

A. Floer, H. Hofer, and D. Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math, J, vol.80, pp.251-292, 1995.

K. Fukaya, Floer homology of Lagrangian submanifolds, Morse Theoretic Methods in Nonlinear Analysis, Nato Science Series, pp.231-276, 2004.

K. Fukaya, Y. Oh, H. Ohta, and K. Ono, Lagrangian intersection Floer theory -anomaly and obstruction, AMS/IP Studies in Advanced Mathematics, 2009.
DOI : 10.1090/amsip/046.2

K. Fukaya, P. Seidel, and I. Smith, Exact Lagrangian submanifolds in simply-connected cotangent bundles, Inventiones mathematicae, vol.9, issue.1, pp.1-27, 2008.
DOI : 10.1007/s00222-007-0092-8

K. Fukaya, P. Seidel, and I. Smith, The symplectic geometry of cotangent bundles from a categorical viewpoint, Homological Mirror Symme-try : New Developments and Perspectives, Notes in Physics, vol.757, p.126, 2008.

A. Gadbled, Obstruction ?? l???existence de plongements lagrangiens monotones dans les fibr??s cotangents de vari??t??s fibr??es au-dessus du cercle, Annales de l???institut Fourier, vol.59, issue.3, pp.1135-1175, 2009.
DOI : 10.5802/aif.2460

M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Inventiones Mathematicae, vol.113, issue.108, pp.307-347, 1985.
DOI : 10.1007/BF01388806

R. Hind, Lagrangian spheres in $$ S^2 \times S^2 $$, Geometric And Functional Analysis, vol.14, issue.2, pp.303-318, 2004.
DOI : 10.1007/s00039-004-0459-6

S. Hu, F. Lalonde, and R. , Leclercq Homological Lagrangian monodromy, 2009.
DOI : 10.2140/gt.2011.15.1617
URL : http://arxiv.org/abs/0912.1325

D. Kwon and Y. Oh, Structure of the image of (pseudo)-holomorphic discs with totally real boundary condition, Communications in Analysis and Geometry, vol.8, issue.1, pp.31-82, 2000.
DOI : 10.4310/CAG.2000.v8.n1.a2

D. Kwon and Y. Oh, Structure of the image of analytic discs attached to totally real submanifolds, The Third Pacific Rim Geometry Conference, Monogr. Geom. Topology, vol.25, pp.139-166, 1996.

F. Lalonde, Suppression lagrangienne de points doubles et rigidit?? symplectique, Journal of Differential Geometry, vol.36, issue.3, pp.747-764, 1992.
DOI : 10.4310/jdg/1214453187

F. Lalonde and J. Sikorav, Sous-vari??t??s lagrangiennes et lagrangiennes exactes des fibr??s cotangents, Commentarii Mathematici Helvetici, vol.66, issue.1, pp.18-33, 1991.
DOI : 10.1007/BF02566634

F. Latour, Existence de l-formes ferm??es non singuli??res dans une classe de cohomologie de de Rham, Publications math??matiques de l'IH??S, vol.45, issue.1, pp.135-194, 1994.
DOI : 10.1007/BF02698899

F. Laudenbach and J. Sikorav, Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibr??? cotangent, Inventiones Mathematicae, vol.84, issue.106, pp.349-357, 1985.
DOI : 10.1007/BF01388807

L. Lazzarini, Decomposition of a J-holomorphic curve, preprint

H. V. Lê and K. Ono, Symplectic fixed points, the Calabi invariant and Novikov homology, Topology, vol.34, issue.1, pp.155-176, 1995.

M. Maydanskiy and P. Seidel, Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres, Journal of Topology, vol.3, issue.1, pp.157-180, 2010.
DOI : 10.1112/jtopol/jtq003

J. Mcleary, A user's guide to spectral sequences, 2001.
DOI : 10.1017/CBO9780511626289

M. Muller, Une structure symplectique sur ???6 avec une sph??re lagrangienne plong??e et un champ de Liouville completavec une sph??re lagrangienne plong??e et un champ de Liouville complet, Commentarii Mathematici Helvetici, vol.65, issue.1, pp.623-663, 1990.
DOI : 10.1007/BF02566630

]. D. Nadler, Microlocal branes are constructible sheaves, arXiv :math/0612399v1 [math, 2006.

S. Nemirovsky, Homology class of a Lagrangian Klein bottle, Izvestiya: Mathematics, vol.73, issue.4, pp.689-698, 2009.
DOI : 10.1070/IM2009v073n04ABEH002462

S. Nemirovsky, Lagrangian Klein Bottles in $${\mathbb{R}^{2n}}$$, Geometric and Functional Analysis, vol.60, issue.4, pp.902-909, 2009.
DOI : 10.1007/s00039-009-0014-6

S. P. Novikov, Multivalued functions and functionals. An analogue of the Morse theory, Soviet. Math. Dokl. vol, vol.24, issue.2, pp.222-226, 1981.

Y. Oh, Floer cohomology of lagrangian intersections and pseudo-holomorphic disks I, Communications on Pure and Applied Mathematics, vol.201, issue.7, pp.949-993, 1993.
DOI : 10.1002/cpa.3160460702

Y. Oh, Floer cohomology of lagrangian intersections and pseudo-holomorphic disks I, Communications on Pure and Applied Mathematics, vol.201, issue.7, pp.949-993, 1993.
DOI : 10.1002/cpa.3160460702

Y. Oh, Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Internat. Math. Res. Notices, vol.7, pp.305-346, 1996.

A. Pajitnov, Surgery on the Novikov complex, K-Theory, vol.10, issue.4, pp.323-412, 1996.
DOI : 10.1007/BF00533216

L. Polterovich, The Maslov class of Lagrange surfaces and Gromov's pseudo-holomorphic curves, Trans. Amer. Math. Soc, vol.325, pp.241-248, 1991.

L. Polterovich, Monotone Lagrange submanifolds of linear spaces and the Maslov class in cotangent bundles, Mathematische Zeitschrift, vol.100, issue.1, pp.217-222, 1991.
DOI : 10.1007/BF02571385

L. Polterovich, The surgery of Lagrangian submanifolds, Geometric and Funtional Analysis, pp.198-210, 1991.

V. Shevchishin, Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups, Izvestiya: Mathematics, vol.73, issue.4, pp.797-859, 2009.
DOI : 10.1070/IM2009v073n04ABEH002465

P. Seidel, Graded lagrangian submanifolds, Bulletin de la Société mathématique de France, vol.128, issue.1, pp.103-149, 2000.
DOI : 10.24033/bsmf.2365

P. Seidel, Exact Lagrangian Submanifolds in T*Sn and the Graded Kronecker Quiver, Int. Math. Ser, vol.3, pp.349-364, 2004.
DOI : 10.1007/0-306-48658-X_8

J. Sikorav, Homologie de Novikov associéè a une classe de cohomologie réelle de degré un, 1987.

J. R. Stallings, On fibering certains 3-manifolds, Topology of 3- manifolds and related topics, N.J, pp.95-100, 1962.

C. Viterbo, Intersection de sous-vari??t??s lagrangiennes, fonctionnelles d'action et indice des syst??mes hamiltoniens, Bulletin de la Société mathématique de France, vol.79, issue.3, pp.361-390, 1987.
DOI : 10.24033/bsmf.2082
URL : http://archive.numdam.org/article/BSMF_1987__115__361_0.pdf

C. Viterbo, A new obstruction to embedding Lagrangian tori, Inventiones Mathematicae, vol.4, issue.1, pp.301-320, 1990.
DOI : 10.1007/BF01231188