  After reviewing recent results on symplectic Lefschetz pencils and symplectic
branched covers of CP^2, we describe a new construction of maps from symplectic
manifolds of any dimension to CP^2 and the associated monodromy invariants. We
also show that a dimensional induction process makes it possible to describe
any compact symplectic manifold by a series of words in braid groups and a word
in a symmetric group.
