 
Summary: Proceedings of 7th
GĻokova
GeometryTopology Conference,
pp, 1 42
Symplectic maps to projective spaces and symplectic
invariants
Denis Auroux
Abstract. After reviewing recent results on symplectic Lefschetz pencils and sym
plectic branched covers of CP2
, we describe a new construction of maps from sym
plectic manifolds of any dimension to CP2
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.
1. Introduction
Let (X2n
, ) be a compact symplectic manifold. We will throughout this text assume
that the cohomology class 1
2 [] H2
