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AUTHOR Kim, Joontae,Kim, Joontae
TITLE The Chekanov torus in S-2 x S-2 is not real
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JOURNAL JOURNAL OF SYMPLECTIC GEOMETRY, 2021
ABSTRACT We prove that the count of Maslov index 2 J-holomorphic discs passing through a generic point of a real Lagrangian submanifold with minimal Maslov number at least two in a closed spherically monotone symplectic manifold must be even. As a corollary, we exhibit a genuine real symplectic phenomenon in terms of involutions, namely that the Chekanov torus T-Chek in S-2 x S-2, which is a monotone Lagrangian torus not Hamiltonian isotopic to the Clifford torus T-Clif, can be seen as the fixed point set of a smooth involution, but not of an antisymplectic involution.
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