Let $f:X\rightarrow B$ be a topological $T^{n}$ fibration and let $U\subset B$ be an open contractible neighborhood of $b\in\Delta$ such that $U\cap\Delta=\{b\}$, when $n=2$; or else, when $n=3$, such that $U$ satisfies $(a)$, $(b)$ or $(c)$ in point $2$ of Assumption 2.2. Let $X_{b_{0}}$ be a fibre over $b_{0}\in U-\Delta$. Consider the monodromy representation

$$\mathcal{M}_{b}:\pi_{1}(U-\Delta,b_{0})\rightarrow SL(H_{1}(X_{b_{0}},\mathbb{Z})).$$

The image of $\mathcal{M}_{b}$ is called the local monodromy group about $X_{b}$ (also denoted by $\mathcal{M}_{b}$).