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Monotone Lagrangian submanifolds of\/ $\mathbb{C}^n$ and toric topology

Vardan Oganesyan

Algebraic & Geometric Topology 22 (2022) 1017–1056
Bibliography
1 D Auroux, Infinitely many monotone Lagrangian tori in 6, Invent. Math. 201 (2015) 909 MR3385637
2 A Bahri, M Bendersky, F R Cohen, S Gitler, The polyhedral product functor: a method of decomposition for moment-angle complexes, arrangements and related spaces, Adv. Math. 225 (2010) 1634 MR2673742
3 A Bahri, M Bendersky, F R Cohen, S Gitler, Operations on polyhedral products and a new topological construction of infinite families of toric manifolds, Homology Homotopy Appl. 17 (2015) 137 MR3426378
4 V M Buchstaber, T E Panov, Toric topology, 204, Amer. Math. Soc. (2015) MR3363157
5 L Cai, S Choi, Integral cohomology groups of real toric manifolds and small covers, Mosc. Math. J. 21 (2021) 467 MR4277852
6 Y V Chekanov, Lagrangian tori in a symplectic vector space and global symplectomorphisms, Math. Z. 223 (1996) 547 MR1421954
7 Y Chekanov, F Schlenk, Notes on monotone Lagrangian twist tori, Electron. Res. Announc. Math. Sci. 17 (2010) 104 MR2735030
8 S Choi, H Park, Multiplicative structure of the cohomology ring of real toric spaces, Homology Homotopy Appl. 22 (2020) 97 MR4027292
9 K Cieliebak, E Goldstein, A note on the mean curvature, Maslov class and symplectic area of Lagrangian immersions, J. Symplectic Geom. 2 (2004) 261 MR2108376
10 M Damian, On the topology of monotone Lagrangian submanifolds, Ann. Sci. École Norm. Sup. 48 (2015) 237 MR3335843
11 J D Evans, J Kędra, Remarks on monotone Lagrangians in n, Math. Res. Lett. 21 (2014) 1241 MR3335845
12 K Fukaya, Application of Floer homology of Langrangian submanifolds to symplectic topology, from: "Morse theoretic methods in nonlinear analysis and in symplectic topology" (editors P Biran, O Cornea, F Lalonde), NATO Sci. Ser. II Math. Phys. Chem. 217, Springer (2006) 231 MR2276953
13 S Gitler, S López de Medrano, Intersections of quadrics, moment-angle manifolds and connected sums, Geom. Topol. 17 (2013) 1497 MR3073929
14 A B Givental, Lagrangian imbeddings of surfaces and unfolded Whitney umbrella, Funktsional. Anal. i Prilozhen. 20 (1986) 35 MR868559
15 V Gómez Gutiérrez, S López de Medrano, Topology of the intersections of quadrics, II, Bol. Soc. Mat. Mex. 20 (2014) 237 MR3264614
16 M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
17 A Haefliger, M W Hirsch, On the existence and classification of differentiable embeddings, Topology 2 (1963) 129 MR149494
18 A Kotelskiy, Minimal and H-minimal submanifolds in toric geometry, J. Symplectic Geom. 14 (2016) 431 MR3531976
19 S López de Medrano, Topology of the intersection of quadrics in n, from: "Algebraic topology" (editors G Carlsson, R L Cohen, H R Miller, D C Ravenel), Lecture Notes in Math. 1370, Springer (1989) 280 MR1000384
20 G Mikhalkin, Examples of tropical-to-Lagrangian correspondence, Eur. J. Math. 5 (2019) 1033 MR3993277
21 A E Mironov, New examples of Hamilton-minimal and minimal Lagrangian manifolds in n and Pn, Mat. Sb. 195 (2004) 89 MR2058378
22 A E Mironov, T E Panov, Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings, Funktsional. Anal. i Prilozhen. 47 (2013) 47 MR3087831
23 S Y Nemirovski, Homology class of a Lagrangian Klein bottle, Izv. Ross. Akad. Nauk Ser. Mat. 73 (2009) 37 MR2583965
24 Y G Oh, Volume minimization of Lagrangian submanifolds under Hamiltonian deformations, Math. Z. 212 (1993) 175 MR1202805
25 Y G Oh, Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Int. Math. Res. Not. 1996 (1996) 305 MR1389956
26 T E Panov, Geometric structures on moment-angle manifolds, Uspekhi Mat. Nauk 68 (2013) 111 MR3113858
27 L Polterovich, The surgery of Lagrange submanifolds, Geom. Funct. Anal. 1 (1991) 198 MR1097259
28 V V Shevchishin, Lagrangian embeddings of the Klein bottle and the combinatorial properties of mapping class groups, Izv. Ross. Akad. Nauk Ser. Mat. 73 (2009) 153 MR2583968
29 R Vianna, On exotic Lagrangian tori in P2, Geom. Topol. 18 (2014) 2419 MR3268780
30 R Vianna, Infinitely many exotic monotone Lagrangian tori in P2, J. Topol. 9 (2016) 535 MR3509972