Symplectic monodromy, quasi-homogeneous polynomials and spectral flow

Details Symplectic monodromy, quasi-homogeneous polynomials and spectral flow Symplectic monodromy, quasi-homogeneous polynomials and spectral flow

2011-04-12

arxiv.org/abs/1104.2095v1

Mathematics

Differential Geometry

31 pages

Scientific paper

We encode the variation structure of a quasihomogeneous polynomial with an isolated singularity as introduced by Nemethi in a set of spectral flows of the signature operator on the Milnor bundle by varying global elliptic boundary conditions in a specific way using the quasihomogeneous circle action on the Brieskorn lattice. For this, we use adiabatic techniques and well-known results on spectral flow and Maslov index. Furthermore we interpret the inequality of a certain member of this family of spectral flows with a spectral flow induced by a Reeb flow on the boundary of the Milnor fibre as giving a sufficient condition for the 'symplectic monodromy' of the fibration to define an element of infinite order in the relative symplectic isotopy group of the Milnor fibre, this uses previous results of P. Seidel resp. of the author. We expect generalizations of the results to wider classes of (algebraic) singularities.

Affiliated with

Also associated with

No associations

Rating

Symplectic monodromy, quasi-homogeneous polynomials and spectral flow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symplectic monodromy, quasi-homogeneous polynomials and spectral flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symplectic monodromy, quasi-homogeneous polynomials and spectral flow will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-730938