arXiv 2109.014352021-09-03math.SG

Chekanov torus and Gelfand--Zeitlin torus in $S^2 \times S^2$

Yoosik Kim

备注：: 12 pages, 1 figure

英文摘要：

The Chekanov torus was the first known \emph{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 $S^2 \times S^2$ and a monotone Lagrangian torus which had been introduced before Chekanov's construction \cite{Chekanov}. We prove that the monotone Lagrangian torus fiber in a certain Gelfand--Zeitlin system is Hamiltonian isotopic to the Chekanov torus in $S^2 \times S^2$.

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