On 4-manifolds fibered by tori. II (Q789058)

[For part I see ibid. 58, 298-301 (1982; Zbl 0515.55012).] In this paper the following signature formula for torus fibrations is proved and some consequences are noted. Theorem. There exists a function \(\sigma\) from the class of topological equivalence classes of singular fibers of torus fibrations to the set \(\{m/3| m\quad an\quad integer\}\) so that if \(\{F_ 1,...,F_ r\}\) is a representative set of all singular fibers of a given torus fibration \(M\to B\), where M is a closed, compact, smooth 4-manifold, then the signature of the homological intersection form \(H_ 2(M;{\mathbb{Z}})\times H_ 2(M;{\mathbb{Z}})\to {\mathbb{Z}}\) is given by \(\sum^{r}_{i=1}\sigma(F_ i)\).