The ℤ–graded symplectic Floer cohomology of monotone Lagrangian sub-manifolds

Li, Weiping¹

¹Department of Mathematics, Oklahoma State University, Stillwater OK 74078-0613, USA

Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 647-684

Résumé

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.

Détail

DOI : 10.2140/agt.2004.4.647

Keywords: monotone Lagrangian submanifold, Maslov index, Floer cohomology, spectral sequence

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