Geometry & Topology Volume 15, issue 1 (2011)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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The topology of toric symplectic manifolds

Dusa McDuff

Geometry & Topology 15 (2011) 145–190

DOI: 10.2140/gt.2011.15.145

Bibliography

1	V V Batyrev, Toric Fano threefolds, Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981) 704, 927 MR631434
2	S Choi, M Masuda, D Y Suh, Topological classification of generalized Bott towers, Trans. Amer. Math. Soc. 362 (2010) 1097 MR2551516
3	S Choi, T Panov, D Y Suh, Toric cohomological rigidity of simple convex polytopes, to appear in J. London Math. Soc. arXiv:0807.4800
4	M W Davis, T Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991) 417 MR1104531
5	T Delzant, Hamiltoniens périodiques et images convexes de l'application moment, Bull. Soc. Math. France 116 (1988) 315 MR984900
6	R Fintushel, R J Stern, Knots, links, and $4$–manifolds, Invent. Math. 134 (1998) 363 MR1650308
7	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian Floer theory on compact toric manifolds. I, Duke Math. J. 151 (2010) 23 MR2573826
8	C Haase, I V Melnikov, The reflexive dimension of a lattice polytope, Ann. Comb. 10 (2006) 211 MR2258235
9	Y Karshon, L Kessler, M Pinsonnault, A compact symplectic four-manifold admits only finitely many inequivalent toric actions, J. Symplectic Geom. 5 (2007) 139 MR2377250
10	J Kȩdra, D McDuff, Homotopy properties of Hamiltonian group actions, Geom. Topol. 9 (2005) 121 MR2115670
11	F Lalonde, D McDuff, L Polterovich, Topological rigidity of Hamiltonian loops and quantum homology, Invent. Math. 135 (1999) 369 MR1666763
12	E Lerman, Symplectic cuts, Math. Res. Lett. 2 (1995) 247 MR1338784
13	M Masuda, Symmetry of a symplectic toric manifold, to appear in J. Symp. Geom. arXiv:0906.4479
14	M Masuda, Equivariant cohomology distinguishes toric manifolds, Adv. Math. 218 (2008) 2005 MR2431667
15	M Masuda, D Y Suh, Classification problems of toric manifolds via topology, from: "Toric topology" (editors M Harada, Y Karson, M Masuda, T Panov), Contemp. Math. 460, Amer. Math. Soc. (2008) 273 MR2428362
16	D McDuff, Displacing Lagrangian toric fibers via probes, to appear in Geom. Topol. arXiv:0904.1686
17	D McDuff, Examples of symplectic structures, Invent. Math. 89 (1987) 13 MR892186
18	D McDuff, Quantum homology of fibrations over $S^2$, Internat. J. Math. 11 (2000) 665 MR1780735
19	D McDuff, L Polterovich, Symplectic packings and algebraic geometry, Invent. Math. 115 (1994) 405 MR1262938
20	D McDuff, D Salamon, $J$–holomorphic curves and quantum cohomology, Univ. Lecture Series 6, Amer. Math. Soc. (1994) MR1286255
21	D McDuff, S Tolman, Topological properties of Hamiltonian circle actions, Int. Math. Res. Pap. (2006) MR2210662
22	D McDuff, S Tolman, Polytopes with mass linear functions. I, Int. Math. Res. Not. (2010) 1506 MR2628835
23	D McDuff, S Tolman, Polytopes with mass linear functions. II, in preparation
24	A Paffenholz, Private communication (2009)
25	A Pelayo, Topology of spaces of equivariant symplectic embeddings, Proc. Amer. Math. Soc. 135 (2007) 277 MR2280203
26	A Pelayo, S Tolman, Fixed points of symplectic periodic flows, to appear in Ergod. Theory Dynam. Systems arXiv:1003.4787
27	M Pinsonnault, Maximal compact tori in the Hamiltonian group of $4$–dimensional symplectic manifolds, J. Mod. Dyn. 2 (2008) 431 MR2417479
28	Y Ruan, Symplectic topology on algebraic $3$–folds, J. Differential Geom. 39 (1994) 215 MR1258920
29	E Shelukhin, Remarks on invariants of Hamiltonian loops, J. Topol. Anal. 2 (2010) 277 MR2718126
30	V A Timorin, An analogue of the Hodge–Riemann relations for simple convex polyhedra, Uspekhi Mat. Nauk 54 (1999) 113 MR1711255
31	K Watanabe, M Watanabe, The classification of Fano $3$–folds with torus embeddings, Tokyo J. Math. 5 (1982) 37 MR670903