Symplectic monodromy, Leray residues and quasi-homogeneous polynomials

Abstract

We formulate certain sufficient conditions for the symplectic monodromy of an isolated quasihomogeneous singularity to be of infinite order in the relative symplectic mapping class group of the Milnor fibre and give a proof using Maslov classes, stability theory for Lagrangian folds resp. stable Morse theory for generating families as well as algebraic results about relative cohomology of smoothings of isolated singularities. Our conditions being slightly more restrictive than Seidel's, in contrary to Seidel's proof, we do not use Floer theory to derive this result. An alternative approach using bounding disks in fibred Lagrangian families is given and its possible application to generalizations to the non-quasihomogeneous case is discussed.

59 pages, erroneous statement in introduction corrected, minor further corrections