Symplectic maps to projective spaces and symplectic invariants

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.

39 pages; to appear in Proc. 7th Gokova Geometry-Topology Conference

Cited by in corpus (7)

• Homological mirror symmetry for the quartic surface
• Fundamental groups of complements of plane curves and symplectic invariants
• A degree doubling formula for braid monodromies and Lefschetz pencils
• The geometry of 2-calibrated manifolds
• Monodromy, vanishing cycles, knots and the adjoint quotient
• Fundamental group for the complement of the Cayley's singularities
• Toward a topological characterization of symplectic manifolds