On monodromy representations in Denham–Suciu fibrations

We study the monodromy representation corresponding to a fibration introduced by G. Denham and A. Suciu [5], 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(Fn)Out(Fn) and SLn(Z)SLn(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(Fn)Out(Fn), 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.