The Z–graded symplectic Floer cohomology of monotone Lagrangian sub–manifolds
نویسنده
چکیده
We define an integer graded symplectic Floer cohomology and a Fintushel–Stern type spectral sequence which are new invariants for monotone Lagrangian sub–manifolds and exact isotopes. The Z–graded symplectic Floer cohomology is an integral lifting of the usual ZΣ(L) –graded Floer–Oh cohomology. We prove the Künneth formula for the spectral sequence and an ring structure on it. The ring structure on the ZΣ(L) –graded Floer cohomology is induced from the ring structure of the cohomology of the Lagrangian sub–manifold via the spectral sequence. Using the Z– graded symplectic Floer cohomology, we show some intertwining relations among the Hofer energy eH(L) of the embedded Lagrangian, the minimal symplectic action σ(L), the minimal Maslov index Σ(L) and the smallest integer k(L, φ) of the converging spectral sequence of the Lagrangian L . AMS Classification 53D40; 53D12, 70H05
منابع مشابه
Lagrangian Embeddings, Maslov Indexes and Integer Graded Symplectic Floer Cohomology
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 ZΣ(L) grading. As one of applications of the spectral sequence, we offer an affirmative answer to an Audin’s question for oriented, ...
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