On exotic monotone Lagrangian tori in $\mathbb{CP}^2$ and $\mathbb{S}_2 \times \mathbb{S}_2$

In this note, we prove that two constructions of exotic monotone Lagrangian tori, namely the one by Chekanov and Schlenk and the one obtained by the circle bundle construction of Biran, are Hamiltonian isotopic in $\mathbb{CP}^2$ and $\mathbb{S}_2 \times \mathbb{S}_2$.

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Published 22 August 2013