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

Yoosik Kim

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arXiv · 2109.01435

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

Yoosik Kim

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Abstract

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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BibTeX RIS

Yoosik Kim. 2021-09-03. Chekanov torus and Gelfand--Zeitlin torus in $S^2 \times S^2$. https://arxiv.org/abs/2109.01435

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