On monodromy representations in Denham-Suciu fibrations

Abstract

We study the monodromy representation corresponding to a fibration introduced by G. Denham and A. Suciu, which involves polyhedral products given in Definition 2.2. Algebraic and geometric descriptions for these monodromy representations are given. In particular, we study the case of a product of two finite cyclic groups and obtain representations into $Out(F_n)$ and $SL_n(\mathbb Z)$. We give algebraic descriptions of monodromy for the case of a product of any two finite groups . Finally we give a geometric description for monodromy representations of a product of 2 or more finite groups to $Out(F_n)$, as well as some algebraic properties. The geometric description does not rely on choosing a basis for the fundamental group of the fibre in terms of commutators, hence avoids this delicate question.