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The Z-graded symplectic Floer cohomology of monotone Lagrangian sub-manifolds | | Weiping Li
; | | Date: |
19 Sep 2004 | | Journal: | Algebr. Geom. Topol. 4 (2004) 647-684 | | Subject: | Geometric Topology; Symplectic Geometry MSC-class: 53D40, 53D12, 70H05 | math.GT math.SG | | Abstract: | 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 Z_Sigma(L)-graded Floer-Oh cohomology. We prove the Kunneth formula for the spectral sequence and an ring structure on it. The ring structure on the Z_Sigma(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 e_H(L) of the embedded Lagrangian, the minimal symplectic action sigma(L), the minimal Maslov index Sigma(L)$ and the smallest integer k(L, phi$ of the converging spectral sequence of the Lagrangian L. | | Source: | arXiv, math.GT/0409332 | | Services: | Forum | Review | PDF | Favorites | |
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