Graded Lagrangian submanifolds

Details Graded Lagrangian submanifolds Graded Lagrangian submanifolds

1999-03-09

arxiv.org/abs/math/9903049v2

Bull. Soc. Math. France 128 (2000), 103-149

Mathematics

Symplectic Geometry

LaTex2e, 32 pages, one eps figure

Scientific paper

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.

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