The map $f:X\rightarrow B$ is a topological $T^{3}$ fibration with discriminant locus $\Delta\subset\Gamma$ such that $f(\Sigma)=\Delta$ satisfying

• (a)

  $(X,\omega,f,B)$ is topologically conjugate to a generic singular fibration.

• (b)

  There is a continuous $S^{1}$ invariant map $G:X\rightarrow M$ such that

  • (i)

    if $G^{\pm}=G|_{X^{\pm}}$ then $G^{+}$ and $G^{-}$ are restrictions of $C^{\infty}$ maps on $X$;

  • (ii)

    $f$ can be written as $f=(\mu,G)$ and $f$ restricted to $X^{\pm}$ is a proper map with connected Lagrangian fibres.

• (c)

  There is a connected, $S^{1}$ invariant, open neighborhood $\mathfrak{U}\subseteq X$ of $\Sigma$ such that $f(\mathfrak{U})=B$ and such that $f_{\mathfrak{U}}=f|_{\mathfrak{U}}$ is a $C^{\infty}$ map with non degenerate singular points.