Let $\mathcal{F}=(X,\omega,f,B)$ be a Lagrangian fibration.

• (i)

  A Lagrangian generic-singular fibration is a smooth Lagrangian fibration $\mathcal{F}$, with non-degenerate singularities (in the sense of [26]) which is conjugate to a topological $T^{3}$ fibration of generic type (cf. Example 2.7).

• (ii)

  A Lagrangian positive fibration is a Lagrangian fibration $\mathcal{F}$ which is conjugate to a topological $T^{3}$ fibration of positive type (cf. Example 2.10).