TY - JOUR
AU - Kim, Joontae
AB - Abstract:In this paper, we classify up to Hamiltonian isotopy Lagrangian tori that split as a product of circles in $S^2 \times S^2$, 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 give many applications, among others: (1) answering a question on Lagrangian 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 $\mathbb{R}^4$.
TI - Lagrangian split tori in $S^2 \times S^2$ and billiards
JF - Mathematics
DO - 10.48550/arxiv.2502.03324
DA - 2025-02-05
UR - https://www.deepdyve.com/lp/arxiv-cornell-university/lagrangian-split-tori-in-s-2-times-s-2-and-billiards-hvcm2VsfId
VL - 2025
IS - 2502
DP - DeepDyve
ER -