Algebraic and Geometric Topology 4 (2004),
paper no. 30, pages 647-684.
The Z-graded symplectic Floer cohomology of monotone Lagrangian sub-manifolds
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.
Monotone Lagrangian sub-manifold, Maslov index, Floer cohomology, spectral sequence
AMS subject classification.
Secondary: 53D12, 70H05.
Submitted: 3 December 2002.
Accepted: 9 August 2004.
Published: 3 September 2004.
Notes on file formats
Department of Mathematics, Oklahoma State University
Stillwater, Oklahoma 74078-0613
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