Abstract

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.