  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.
