Symplectic triangle inequality

Shevchishin, Vsevolod; Smirnov, Gleb

doi:10.1090/proc/14842

Symplectic triangle inequality
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by Vsevolod Shevchishin and Gleb Smirnov PDF

Proc. Amer. Math. Soc. 148 (2020), 1389-1397 Request permission

Abstract:

We prove a non-squeezing result for Lagrangian embeddings of the real projective plane into blow-ups of the symplectic ball.

References

Michèle Audin, Quelques remarques sur les surfaces lagrangiennes de Givental′, J. Geom. Phys. 7 (1990), no. 4, 583–598 (1991) (French, with English summary). MR 1131914, DOI 10.1016/0393-0440(90)90008-Q
Matthew Strom Borman, Tian-Jun Li, and Weiwei Wu, Spherical Lagrangians via ball packings and symplectic cutting, Selecta Math. (N.S.) 20 (2014), no. 1, 261–283. MR 3182449, DOI 10.1007/s00029-013-0120-z
Ronald Fintushel and Ronald J. Stern, Rational blowdowns of smooth $4$-manifolds, J. Differential Geom. 46 (1997), no. 2, 181–235. MR 1484044
Robert E. Gompf, A new construction of symplectic manifolds, Ann. of Math. (2) 142 (1995), no. 3, 527–595. MR 1356781, DOI 10.2307/2118554
M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347. MR 809718, DOI 10.1007/BF01388806
R. Hind and E. Opshtein, Squeezing Lagrangian tori in dimension $4$, Preprint, arXiv:1901.02124.
T. Khodorovsky, Symplectic Rational Blow-up, Preprint, arXiv:1303.2581v1.
Tatyana Khodorovskiy, Smooth embeddings of rational homology balls, Topology Appl. 161 (2014), 386–396. MR 3132378, DOI 10.1016/j.topol.2013.10.039
François Lalonde and Dusa McDuff, The classification of ruled symplectic $4$-manifolds, Math. Res. Lett. 3 (1996), no. 6, 769–778. MR 1426534, DOI 10.4310/MRL.1996.v3.n6.a5
Tian-Jun Li and Ai-Ko Liu, Uniqueness of symplectic canonical class, surface cone and symplectic cone of 4-manifolds with $B^+=1$, J. Differential Geom. 58 (2001), no. 2, 331–370. MR 1913946
John D. McCarthy and Jon G. Wolfson, Symplectic normal connect sum, Topology 33 (1994), no. 4, 729–764. MR 1293308, DOI 10.1016/0040-9383(94)90006-X
Tian-Jun Li and Weiwei Wu, Lagrangian spheres, symplectic surfaces and the symplectic mapping class group, Geom. Topol. 16 (2012), no. 2, 1121–1169. MR 2946805, DOI 10.2140/gt.2012.16.1121
S. Yu. Nemirovskiĭ, The homology class of a Lagrangian Klein bottle, Izv. Ross. Akad. Nauk Ser. Mat. 73 (2009), no. 4, 37–48 (Russian, with Russian summary); English transl., Izv. Math. 73 (2009), no. 4, 689–698. MR 2583965, DOI 10.1070/IM2009v073n04ABEH002462
Margaret Symington, Symplectic rational blowdowns, J. Differential Geom. 50 (1998), no. 3, 505–518. MR 1690738
Margaret Symington, Four dimensions from two in symplectic topology, Topology and geometry of manifolds (Athens, GA, 2001) Proc. Sympos. Pure Math., vol. 71, Amer. Math. Soc., Providence, RI, 2003, pp. 153–208. MR 2024634, DOI 10.1090/pspum/071/2024634
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), no. 4, 153–224 (Russian, with Russian summary); English transl., Izv. Math. 73 (2009), no. 4, 797–859. MR 2583968, DOI 10.1070/IM2009v073n04ABEH002465