Lagrangian split tori in S<SUP>2</SUP> x S<SUP>2</SUP> and billiards

초록

In this paper, we classify up to Hamiltonian isotopy Lagrangian tori that split as a product of circles in S-2 x S-2, when the latter is equipped with a non-monotone split symplectic form. We show that this classification is equivalent to a problem of mathematical billiards in rectangles. We givemany applications, amongothers: (1) answering a question onLagrangian packing numbers raised by Polterovich-Shelukhin, (2) studying the topology of the space of Lagrangian tori, and (3) determining which split tori are images under symplectic ball embeddings of Chekanov or product tori in R-4.

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