Graded Lagrangian submanifolds
Symplectic Geometry
2007-05-23 v2
Abstract
In the usual setup, the grading on Floer homology is relative: it is unique only up to adding a constant. "Graded Lagrangian submanifolds" are Lagrangian submanifolds with a bit of extra structure, which fixes the ambiguity in the grading. The idea is originally due to Kontsevich. This paper contains an exposition of the theory. Several applications are given, amongst them: (1) topological restrictions on Lagrangian submanifolds of projective space, (2) the existence of "symplectically knotted" Lagrangian spheres on a K3 surface, (3) a result about the symplectic monodromy of weighted homogeneous hypersurface singularities. Revised version: minor modifications, journal reference added.
Cite
@article{arxiv.math/9903049,
title = {Graded Lagrangian submanifolds},
author = {Paul Seidel},
journal= {arXiv preprint arXiv:math/9903049},
year = {2007}
}
Comments
LaTex2e, 32 pages, one eps figure