Algebraic & Geometric Topology Volume 21, issue 5 (2021)

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A monotone Lagrangian casebook

Jack Smith

Algebraic & Geometric Topology 21 (2021) 2273–2312

DOI: 10.2140/agt.2021.21.2273

Bibliography

1	A Amarzaya, Y Ohnita, Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces, Tohoku Math. J. 55 (2003) 583 MR2017227
2	L Astey, S Gitler, E Micha, G Pastor, Cohomology of complex projective Stiefel manifolds, Canad. J. Math. 51 (1999) 897 MR1718684
3	D Auroux, Mirror symmetry and T–duality in the complement of an anticanonical divisor, J. Gökova Geom. Topol. 1 (2007) 51 MR2386535
4	P F Baum, W Browder, The cohomology of quotients of classical groups, Topology 3 (1965) 305 MR189063
5	P Biran, Lagrangian non-intersections, Geom. Funct. Anal. 16 (2006) 279 MR2231465
6	P Biran, K Cieliebak, Symplectic topology on subcritical manifolds, Comment. Math. Helv. 76 (2001) 712 MR1881704
7	P Biran, O Cornea, Quantum structures for Lagrangian submanifolds, preprint (2007) arXiv:0708.4221
8	P Biran, O Cornea, Rigidity and uniruling for Lagrangian submanifolds, Geom. Topol. 13 (2009) 2881 MR2546618
9	P Biran, M Khanevsky, A Floer–Gysin exact sequence for Lagrangian submanifolds, Comment. Math. Helv. 88 (2013) 899 MR3134415
10	A Borel, Sur l’homologie et la cohomologie des groupes de Lie compacts connexes, Amer. J. Math. 76 (1954) 273 MR64056
11	Y V Chekanov, Lagrangian tori in a symplectic vector space and global symplectomorphisms, Math. Z. 223 (1996) 547 MR1421954
12	Y Chekanov, F Schlenk, Notes on monotone Lagrangian twist tori, Electron. Res. Announc. Math. Sci. 17 (2010) 104 MR2735030
13	R Chiang, New Lagrangian submanifolds of ℂPⁿ, Int. Math. Res. Not. 2004 (2004) 2437 MR2076100
14	C H Cho, Holomorphic discs, spin structures, and Floer cohomology of the Clifford torus, Int. Math. Res. Not. 2004 (2004) 1803 MR2057871
15	K Cieliebak, A R Gaio, D A Salamon, J–holomorphic curves, moment maps, and invariants of Hamiltonian group actions, Int. Math. Res. Not. 2000 (2000) 831 MR1777853
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	M Entov, L Polterovich, Rigid subsets of symplectic manifolds, Compos. Math. 145 (2009) 773 MR2507748
18	J D Evans, Y Lekili, Floer cohomology of the Chiang Lagrangian, Selecta Math. 21 (2015) 1361 MR3397452
19	J D Evans, Y Lekili, Generating the Fukaya categories of Hamiltonian G–manifolds, J. Amer. Math. Soc. 32 (2019) 119 MR3868001
20	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
21	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, 46, Amer. Math. Soc. (2009) MR2553465
22	A Gadbled, On exotic monotone Lagrangian tori in ℂP² and 𝕊² × 𝕊², J. Symplectic Geom. 11 (2013) 343 MR3100797
23	H Hopf, Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen, Ann. of Math. 42 (1941) 22 MR4784
24	H Iriyeh, Symplectic topology of Lagrangian submanifolds of ℂPⁿ with intermediate minimal Maslov numbers, Adv. Geom. 17 (2017) 247 MR3652243
25	D McDuff, S Tolman, Topological properties of Hamiltonian circle actions, Int. Math. Res. Pap. 2006 (2006) MR2210662
26	J Oakley, M Usher, On certain Lagrangian submanifolds of S² × S² and ℂPⁿ, Algebr. Geom. Topol. 16 (2016) 149 MR3470699
27	Y G Oh, Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Int. Math. Res. Not. 1996 (1996) 305 MR1389956
28	T Perutz, A symplectic Gysin sequence, preprint (2008) arXiv:0807.1863
29	S Piunikhin, D Salamon, M Schwarz, Symplectic Floer–Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
30	P Seidel, π₁ of symplectic automorphism groups and invertibles in quantum homology rings, Geom. Funct. Anal. 7 (1997) 1046 MR1487754
31	P Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000) 103 MR1765826
32	V de Silva, Products in the symplectic Floer homology of Lagrangian intersections, PhD thesis, University of Oxford (1999)
33	I Smith, Floer cohomology and pencils of quadrics, Invent. Math. 189 (2012) 149 MR2929086
34	J Smith, Floer cohomology of Platonic Lagrangians, J. Symplectic Geom. 17 (2019) 477 MR3992723
35	J Smith, Discrete and continuous symmetries in monotone Floer theory, Selecta Math. 26 (2020) MR4117998
36	B Torricelli, A survey on the Lagrangian SU(n)∕(ℤ∕n) in ℂP^n²−1 , Master’s thesis, University College London (2016)
37	K Wehrheim, C T Woodward, Quilted Floer cohomology, Geom. Topol. 14 (2010) 833 MR2602853
38	K Wehrheim, C Woodward, Orientations for pseudoholomorphic quilts, preprint (2015) arXiv:1503.07803
39	E Witten, The Verlinde algebra and the cohomology of the Grassmannian, from: "Geometry, topology, and physics" (editor S T Yau), Conf. Proc. Lect. Notes Geom. Topol. 4, International (1995) 357 MR1358625
40	F Zapolsky, Quasi-morphisms on contactomorphism groups and Grassmannians of 2–planes, Geom. Dedicata 207 (2020) 287 MR4117574