Geometry & Topology Volume 18, issue 2 (2014)

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Unlinking and unknottedness of monotone Lagrangian submanifolds

Georgios Dimitroglou Rizell and Jonathan David Evans

Geometry & Topology 18 (2014) 997–1034

DOI: 10.2140/gt.2014.18.997

Bibliography

1	P Albers, On the extrinsic topology of Lagrangian submanifolds, Int. Math. Res. Not. (2005) 2341 MR2180810
2	P Albers, Erratum for “On the extrinsic topology of Lagrangian submanifolds”, Int. Math. Res. Not. (2010) 1363 MR2609024
3	V I Arnol’d, On a characteristic class entering into conditions of quantization, Funkcional. Anal. i Priložen. 1 (1967) 1 MR0211415
4	M Audin, F Lalonde, L Polterovich, Symplectic rigidity: Lagrangian submanifolds, from: "Holomorphic curves in symplectic geometry" (editors M Audin, J Lafontaine), Progr. Math. 117, Birkhäuser (1994) 271 MR1274934
5	P Biran, K Cieliebak, Lagrangian embeddings into subcritical Stein manifolds, Israel J. Math. 127 (2002) 221 MR1900700
6	P Biran, O Cornea, A Lagrangian quantum homology, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 1 MR2555932
7	M S Borman, T J Li, W Wu, Spherical Lagrangians via ball packings and symplectic cutting, arXiv:1211.5952
8	V Borrelli, New examples of Lagrangian rigidity, Israel J. Math. 125 (2001) 221 MR1853812
9	R Bott, Lectures on Morse theory, old and new, Bull. Amer. Math. Soc. 7 (1982) 331 MR663786
10	F Bourgeois, A Morse–Bott approach to contact homology, from: "Symplectic and contact topology: Interactions and perspectives" (editors Y Eliashberg, B Khesin, F Lalonde), Fields Inst. Commun. 35, Amer. Math. Soc. (2003) 55 MR1969267
11	F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
12	L Buhovsky, The Maslov class of Lagrangian tori and quantum products in Floer cohomology, J. Topol. Anal. 2 (2010) 57 MR2646989
13	Y Chekanov, F Schlenk, Notes on monotone Lagrangian twist tori, Electron. Res. Announc. Math. Sci. 17 (2010) 104 MR2735030
14	K Cieliebak, U A Frauenfelder, A Floer homology for exact contact embeddings, Pacific J. Math. 239 (2009) 251 MR2461235
15	K Cieliebak, K Mohnke, Compactness for punctured holomorphic curves, J. Symplectic Geom. 3 (2005) 589 MR2235856
16	M Damian, Floer homology on the universal cover, Audin's conjecture and other constraints on Lagrangian submanifolds, Comment. Math. Helv. 87 (2012) 433 MR2914855
17	D L Dragnev, Fredholm theory and transversality for noncompact pseudoholomorphic maps in symplectizations, Comm. Pure Appl. Math. 57 (2004) 726 MR2038115
18	Y Eliashberg, L Polterovich, Unknottedness of Lagrangian surfaces in symplectic $4$–manifolds, Internat. Math. Res. Notices (1993) 295 MR1248704
19	Y Eliashberg, L Polterovich, New applications of Luttinger's surgery, Comment. Math. Helv. 69 (1994) 512 MR1303225
20	Y Eliashberg, L Polterovich, Local Lagrangian $2$–knots are trivial, Ann. of Math. 144 (1996) 61 MR1405943
21	Y Eliashberg, L Polterovich, The problem of Lagrangian knots in four-manifolds, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 313 MR1470735
22	J D Evans, Lagrangian spheres in del Pezzo surfaces, J. Topol. 3 (2010) 181 MR2608481
23	J D Evans, J Kędra, Remarks on monotone Lagrangians in $\mathbb{C}^n$, arXiv:1110.0927
24	K Groh, M Schwarz, K Smoczyk, K Zehmisch, Mean curvature flow of monotone Lagrangian submanifolds, Math. Z. 257 (2007) 295 MR2324804
25	M L Gromov, A topological technique for the construction of solutions of differential equations and inequalities, from: "Actes du Congrès International des Mathématiciens, tome 2", Gauthier-Villars (1971) 221 MR0420697
26	A Haefliger, M W Hirsch, On the existence and classification of differentiable embeddings, Topology 2 (1963) 129 MR0149494
27	R Hind, Lagrangian spheres in $S^2\times S^2$, Geom. Funct. Anal. 14 (2004) 303 MR2060197
28	R Hind, Lagrangian unknottedness in Stein surfaces, Asian J. Math. 16 (2012) 1 MR2904911
29	R Hind, A Ivrii, Isotopies of high genus Lagrangian surfaces, arXiv:math/0602475
30	M A Kervaire, Some nonstable homotopy groups of Lie groups, Illinois J. Math. 4 (1960) 161 MR0113237
31	L Lazzarini, Existence of a somewhere injective pseudo-holomorphic disc, Geom. Funct. Anal. 10 (2000) 829 MR1791142
32	L Lazzarini, Relative frames on $J$–holomorphic curves, J. Fixed Point Theory Appl. 9 (2011) 213 MR2821362
33	J A Lees, On the classification of Lagrange immersions, Duke Math. J. 43 (1976) 217 MR0410764
34	T J Li, W Wu, Lagrangian spheres, symplectic surfaces and the symplectic mapping class group, Geom. Topol. 16 (2012) 1121 MR2946805
35	K M Luttinger, Lagrangian tori in $\mathbf{R}^4$, J. Differential Geom. 42 (1995) 220 MR1366546
36	L A Lyusternik, A I Fet, Variational problems on closed manifolds, Doklady Akad. Nauk SSSR 81 (1951) 17 MR0044760
37	Y G Oh, Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks I, Comm. Pure Appl. Math. 46 (1993) 949 MR1223659
38	L Polterovich, The surgery of Lagrange submanifolds, Geom. Funct. Anal. 1 (1991) 198 MR1097259
39	V V Prasolov, Elements of homology theory, Graduate Studies in Mathematics 81, Amer. Math. Soc. (2007) MR2313004
40	J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827 MR1241874
41	R Siefring, Relative asymptotic behavior of pseudoholomorphic half-cylinders, Comm. Pure Appl. Math. 61 (2008) 1631 MR2456182