S2中的Chekanov环和Gelfand-Zeitlin环 × S2

IF 0.6 4区 数学 Q3 MATHEMATICS
Yoosik Kim
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引用次数: 0

摘要

契卡诺夫环是已知的第一个奇异环,一个单调拉格朗日环,它不是标准单调拉格朗日环的哈密顿同位素。我们探讨了S2×S2中的契卡诺夫环面与契卡诺夫构造之前已经构造的单调拉格朗日环面之间的关系[6]。我们用一种复形性证明了某Gelfand-Zeitlin系统中的单调拉格朗日环面纤维与S2×S2中的契卡诺夫环面存在关联。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Chekanov torus and Gelfand–Zeitlin torus in S2 × S2

The Chekanov torus is the first known exotic torus, a monotone Lagrangian torus that is not Hamiltonian isotopic to the standard monotone Lagrangian torus. We explore the relationship between the Chekanov torus in S2×S2 and a monotone Lagrangian torus that had been constructed before Chekanov's construction [6]. We prove that the monotone Lagrangian torus fiber in a certain Gelfand–Zeitlin system is related to the Chekanov torus in S2×S2 by a symplectomorphism.

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来源期刊
CiteScore
1.00
自引率
20.00%
发文量
81
审稿时长
6-12 weeks
期刊介绍: Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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