  Symplectic four-manifolds give rise to Lefschetz fibrations, which are
determined by monodromy representations of free groups in mapping class groups.
We study the topology of Lefschetz fibrations by analysing the action of the
monodromy on the universal cover of a smooth fibre. We give new and simple
proofs that Lefschetz fibrations arising from pencils (i.e. with exceptional
sections) never split as non-trivial fibre sums, and that no simple closed
curve can be invariant to isotopy under the monodromy representation.
