On the Monodromy of a Multivalued Function Along Its Ramification Locus

We consider multivalued analytic functions in $\mathbb{C}^n$ whose set of singular points occupies a very small part of $\mathbb{C}^n$. Under a mapping of a topological space $Y$ into $\mathbb{C}^n$, such a function $f$ can induce a multivalued function on $Y$. This is possible even if the image of $Y$ entirely lies in the ramification set of $f$. We estimate the monodromy group of the induced function via the monodromy group of $f$.