Proof of the Theorem. Let us pick up a small circle $[\gamma_{x_{0}}]\in H_{1}(B_{1},{\bf Z})$ around $x_{0}$. Then $\sum_{x\in B^{sing}}[\gamma_{x}]+[\gamma_{x_{0}}]=0$. The monodromy around $x_{0}$ can be easily computed via the winding number of the induced vector field (section of $E_{|\gamma_{x_{0}}}$) and is equal to $-\chi(B)u$. Applying homomorphism $i$ we obtain the result. $\blacksquare$