Symplectic rigidity of real and complex polydiscs

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Wong, Yat-Sen¹ 

[1] 1409 W Green St, Urbana, IL 61801 USA

关键词: Symplectic geometry;    Pseudo-holomorphic curve;    Complex analytic set;    Symplectic embedding;    Almost complex structure;   

DOI  :  10.1016/j.jmaa.2017.11.008

来源: Elsevier

【 摘 要 】

In R-2n with its standard symplectic structure, the complex polydisc, D-C(2n)(r), is constructed as the product of n open complex discs of radius r. When n = 2, the real polydisc, D-R(4)(r), is constructed as the product of 2 open real/Lagrangian discs of radius r. Sukhov and Tumanov recently showed that D-C(4)(1) and D-R(4)(1) are not symplectically equivalent. We extend this result in two ways. First we give the necessary and sufficient conditions for an orthogonal image of D-C(4)(1) to be symplectically equivalent to D-C(4)(1). Second, we show that for all r >= 1 and n >= 1, DR4 (1) x D-C(2n-4) (r) is not symplectically equivalent to D-C(4) (1) x D-C(2n-4) (r). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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