We attempt to define a new invariant I of (almost) Calabi-Yau 3-folds M, by counting special
Lagrangian rational homology 3-spheres N in M in each 3-homology class, with a certain
weight w (N) depending on the topology of N. This is motivated by the Gromov–Witten
invariants of a symplectic manifold, which count the J-holomorphic curves in each 2-
homology class. In order for this invariant to be interesting, it should either be unchanged by
deformations of the underlying (almost) Calabi-Yau structure, or else trans-form according to …