Geometry & Topology Volume 13, issue 5 (2009)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Rigidity and uniruling for Lagrangian submanifolds

Paul Biran and Octav Cornea

Geometry & Topology 13 (2009) 2881–2989

DOI: 10.2140/gt.2009.13.2881

Bibliography

1	P Albers, A Lagrangian Piunikhin–Salamon–Schwarz morphism and two comparison homomorphisms in Floer homology arXiv:math/0512037
2	P Albers, On the extrinsic topology of Lagrangian submanifolds, Int. Math. Res. Not. (2005) 2341 MR2180810
3	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
4	J F Barraud, O Cornea, Homotopic dynamics in 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) 109 MR2276950
5	J F Barraud, O Cornea, Lagrangian intersections and the Serre spectral sequence, Ann. of Math. $(2)$ 166 (2007) 657 MR2373371
6	A Beauville, Quantum cohomology of complete intersections, Mat. Fiz. Anal. Geom. 2 (1995) 384 MR1484335
7	P Biran, Lagrangian barriers and symplectic embeddings, Geom. Funct. Anal. 11 (2001) 407 MR1844078
8	P Biran, Lagrangian non-intersections, Geom. Funct. Anal. 16 (2006) 279 MR2231465
9	P Biran, K Cieliebak, Symplectic topology on subcritical manifolds, Comment. Math. Helv. 76 (2001) 712 MR1881704
10	P Biran, K Cieliebak, Lagrangian embeddings into subcritical Stein manifolds, Israel J. Math. 127 (2002) 221 MR1900700
11	P Biran, O Cornea, in preparation
12	P Biran, O Cornea, Quantum structures for Lagrangian submanifolds arXiv:0708.4221
13	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, Amer. Math. Soc. (2009)
14	L Blechman, L Polterovich, private communication
15	L Buhovsky, Multiplicative structures in Lagrangian Floer homology arXiv:math.SG/0608063
16	L Buhovsky, One explicit construction of a relative packing arXiv:0803.2774v3
17	L Buhovsky, Homology of Lagrangian submanifolds in cotangent bundles, Israel J. Math. 143 (2004) 181 MR2106982
18	Y V Chekanov, Lagrangian tori in a symplectic vector space and global symplectomorphisms, Math. Z. 223 (1996) 547 MR1421954
19	Y V Chekanov, F Schlenk, Monotone Lagrangian tori in $\mathbb{R}^{2n}$, $\mathbb{C}P^n$ and products of spheres, in preparation
20	R Chiang, New Lagrangian submanifolds of $\mathbb{CP}^n$, Int. Math. Res. Not. (2004) 2437 MR2076100
21	C H Cho, Holomorphic discs, spin structures, and Floer cohomology of the Clifford torus, Int. Math. Res. Not. (2004) 1803 MR2057871
22	C H Cho, Products of Floer cohomology of torus fibers in toric Fano manifolds, Comm. Math. Phys. 260 (2005) 613 MR2183959
23	C H Cho, Y G Oh, Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds, Asian J. Math. 10 (2006) 773 MR2282365
24	O Cornea, F Lalonde, Cluster homology arXiv:math/0508345
25	O Cornea, F Lalonde, Cluster homology: an overview of the construction and results, Electron. Res. Announc. Amer. Math. Soc. 12 (2006) 1 MR2200949
26	O Cornea, A Ranicki, Rigidity and gluing for Morse and Novikov complexes, J. Eur. Math. Soc. $($JEMS$)$ 5 (2003) 343 MR2017851
27	Y Eliashberg, Topological characterization of Stein manifolds of dimension $\gt 2$, Internat. J. Math. 1 (1990) 29 MR1044658
28	Y Eliashberg, M Gromov, Convex symplectic manifolds, from: "Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989)" (editors E Bedford, J P D’Angelo, R E Greene, S G Krantz), Proc. Sympos. Pure Math. 52, Amer. Math. Soc. (1991) 135 MR1128541
29	Y Eliashberg, L Polterovich, The problem of Lagrangian knots in four-manifolds, from: "Geometric topology (Athens, GA, 1993)" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 313 MR1470735
30	M Entov, L Polterovich, Rigid subsets of symplectic manifolds, Compos. Math. 145 (2009) 773 MR2507748
31	U Frauenfelder, Gromov convergence of pseudoholomorphic disks, J. Fixed Point Theory Appl. 3 (2008) 215 MR2434448
32	K Fukaya, Morse homotopy and its quantization, from: "Geometric topology (Athens, GA, 1993)" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 409 MR1470740
33	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory – anomaly and obstruction, Preprint
34	P Griffiths, J Harris, Principles of algebraic geometry, Pure and Applied Math., Wiley-Interscience (1978) MR507725
35	M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
36	D Kwon, Y G Oh, Structure of the image of (pseudo)-holomorphic discs with totally real boundary condition, Comm. Anal. Geom. 8 (2000) 31 MR1730896
37	L Lazzarini, Relative frames on $J$–holomorphic curves, to appear in J. Fixed Point Theory Appl.
38	L Lazzarini, Existence of a somewhere injective pseudo-holomorphic disc, Geom. Funct. Anal. 10 (2000) 829 MR1791142
39	D McDuff, Hamiltonian $S^{1}$–manifolds are uniruled arXiv:0706.0675v2
40	D McDuff, D Salamon, $J$–holomorphic curves and symplectic topology, Amer. Math. Soc. Colloq. Publ. 52, Amer. Math. Soc. (2004) MR2045629
41	Y G Oh, Mini-max theory, spectral invariants and geometry of the Hamiltonian diffeomorphism group arXiv:math/0206092
42	Y G Oh, Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I, Comm. Pure Appl. Math. 46 (1993) 949 MR1223659
43	Y G Oh, Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Internat. Math. Res. Notices (1996) 305 MR1389956
44	Y G Oh, Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 201 MR1432465
45	Y G Oh, Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, from: "The breadth of symplectic and Poisson geometry" (editors J E Marsden, T S Ratiu), Progr. Math. 232, Birkhäuser (2005) 525 MR2103018
46	Y G Oh, Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group, Duke Math. J. 130 (2005) 199 MR2181090
47	Y G Oh, Lectures on Floer theory and spectral invariants of Hamiltonian flows, 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) 321 MR2276955
48	S Piunikhin, D Salamon, M Schwarz, Symplectic Floer-Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
49	M Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000) 419 MR1755825
50	P Seidel, $\pi_1$ of symplectic automorphism groups and invertibles in quantum homology rings, Geom. Funct. Anal. 7 (1997) 1046 MR1487754
51	P Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000) 103 MR1765826
52	P Seidel, Exact Lagrangian submanifolds in $T^{}S^n$ and the graded Kronecker quiver*, from: "Different faces of geometry" (editors S Donaldson, Y Eliashberg, M Gromov), Int. Math. Ser. 3, Kluwer/Plenum (2004) 349 MR2103000
53	C Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992) 685 MR1157321