What is a monotone Lagrangian cobordism?
Séminaire de théorie spectrale et géométrie, Tome 31 (2012-2014), pp. 43-53.

We explain the notion of Lagrangian cobordism. A flexibility/rigidity dichotomy is illustrated by considering Lagrangian tori in 2 . Towards the end, we present a recent construction by Cornea and the author [8], of monotone cobordisms that are not trivial in a suitable sense.

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     author = {Charette, Fran\c{c}ois},
     title = {What is a monotone {Lagrangian} cobordism?},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {43--53},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
     year = {2012-2014},
     doi = {10.5802/tsg.293},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/tsg.293/}
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Charette, François. What is a monotone Lagrangian cobordism?. Séminaire de théorie spectrale et géométrie, Tome 31 (2012-2014), pp. 43-53. doi : 10.5802/tsg.293. http://www.numdam.org/articles/10.5802/tsg.293/

[1] Arnol’d, V. I. Lagrange and Legendre cobordisms. I, Funktsional. Anal. i Prilozhen., Volume 14 (1980) no. 3, p. 1-13, 96 | MR 583797 | Zbl 0448.57017

[2] Arnol’d, V. I. Lagrange and Legendre cobordisms. II, Funktsional. Anal. i Prilozhen., Volume 14 (1980) no. 4, p. 8-17, 95 | MR 595724 | Zbl 0472.55002

[3] Arnol’d, V. I. Mathematical methods of classical mechanics, Graduate Texts in Mathematics, 60, Springer-Verlag, New York, 1995, pp. xvi+516 Translated from the 1974 Russian original by K. Vogtmann and A. Weinstein, Corrected reprint of the second (1989) edition | MR 997295 | Zbl 0386.70001

[4] Audin, Michèle Cobordismes d’immersions lagrangiennes et legendriennes, Travaux en Cours [Works in Progress], 20, Hermann, Paris, 1987, pp. xvi+203 | MR 903652 | Zbl 0615.57001

[5] Auroux, Denis Mirror symmetry and T-duality in the complement of an anticanonical divisor, J. Gökova Geom. Topol. GGT, Volume 1 (2007), pp. 51-91 | MR 2386535 | Zbl 1181.53076

[6] Biran, Paul; Cornea, Octav Lagrangian cobordism. I, J. Amer. Math. Soc., Volume 26 (2013) no. 2, pp. 295-340 | Article | MR 3011416 | Zbl 1272.53071

[7] Biran, Paul; Cornea, Octav Lagrangian cobordism and Fukaya categories, Geom. Funct. Anal., Volume 24 (2014) no. 6, pp. 1731-1830 | Article | MR 3283928

[8] Charette, Francois; Cornea, Octav Categorification of Seidel’s representation (2014) (To appear in Israel Journal of Mathematics. Available at http://arxiv.org/abs/1307.7235)

[9] Chekanov, Yu. V. Lagrangian embeddings and Lagrangian cobordism, Topics in singularity theory (Amer. Math. Soc. Transl. Ser. 2), Volume 180, Amer. Math. Soc., Providence, RI, 1997, pp. 13-23 | MR 1767110 | Zbl 0933.53038

[10] Chekanov, Yuri; Schlenk, Felix Notes on monotone Lagrangian twist tori, Electron. Res. Announc. Math. Sci., Volume 17 (2010), pp. 104-121 | Article | MR 2735030 | Zbl 1201.53083

[11] Eliashberg, J. Cobordisme des solutions de relations différentielles, South Rhone seminar on geometry, I (Lyon, 1983) (Travaux en Cours), Hermann, Paris, 1984, pp. 17-31 | MR 753850 | Zbl 0542.57024

[12] Frauenfelder, Urs Gromov convergence of pseudoholomorphic disks, J. Fixed Point Theory Appl., Volume 3 (2008) no. 2, pp. 215-271 | Article | MR 2434448 | Zbl 1153.53057

[13] Gromov, Mikhael Pseudoholomorphic curves in symplectic manifolds, Invent. Math., Volume 82 (1985) no. 2, pp. 307-347 | Article | EuDML 143289 | MR 809718 | Zbl 0592.53025

[14] Gromov, Mikhael Partial differential relations, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 9, Springer-Verlag, Berlin, 1986, pp. x+363 | Article | MR 864505 | Zbl 0651.53001

[15] Hyvrier, Clement Lagrangian circle actions (2013) (Preprint. Available at http://arxiv.org/abs/1307.8196) | MR 3523040

[16] Lees, J. Alexander On the classification of Lagrange immersions, Duke Math. J., Volume 43 (1976) no. 2, pp. 217-224 | MR 410764 | Zbl 0329.58006

[17] McDuff, Dusa; Salamon, Dietmar Introduction to symplectic topology, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1998, pp. x+486 | MR 1698616 | Zbl 0844.58029

[18] Polterovich, Leonid The surgery of Lagrange submanifolds, Geom. Funct. Anal., Volume 1 (1991) no. 2, pp. 198-210 | Article | EuDML 58116 | MR 1097259 | Zbl 0754.57027

[19] Polterovich, Leonid The geometry of the group of symplectic diffeomorphisms, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2001, pp. xii+132 | Article | MR 1826128 | Zbl 1197.53003

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