We study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas from family Floer theory and tropical geometry to obtain both obstructions to and constructions of cobordisms; in particular, we give examples of symplectic tori in which the cobordism group has no non-trivial cobordism relations between pairwise distinct fibres, and ones in which the degree zero fibre cobordism group is a divisible group. The results are independent of but motivated by mirror symmetry, and a relation to rational equivalence of 0-cycles on the mirror rigid analytic space.

中文翻译：

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拉格朗日坐标系和热带曲线

我们研究辛格流形中的拉格朗日圆环纤维的圆柱拉格朗日同色性群，这是光滑拉格朗日圆环纤维化的总空间。我们使用家庭Floer理论和热带几何学的思想来获得对鸟粪的阻碍和构造。特别是，我们给出了辛托里的例子，其中在同心圆托组中成对的不同纤维之间不存在非平凡的同心关系，而在其中零度纤维同心性组是可分割的组。结果与镜像对称无关，但受镜像对称性的影响，并且与镜像刚性解析空间上0圈的有理等效性有关。