Lagrangian embedding, Maslov indexes and Integer graded symplectic Floer cohomology

Details Lagrangian embedding, Maslov indexes and Integer graded symplectic Floer cohomology Lagrangian embedding, Maslov indexes and Integer graded symplectic Floer cohomology

1996-02-19

arxiv.org/abs/dg-ga/9602009v2

Mathematics

Differential Geometry

24 pages, amslatex

Scientific paper

We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with $Z_{\Si (L)}$ grading. As one of applications of the spectral sequence, we offer an affirmative answer to an Audin's question for oriented, embedded, monotone Lagrangian tori, i.e. $\Si (L) = 2$.

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