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2004 The $\mathbb{Z}$–graded symplectic Floer cohomology of monotone Lagrangian sub-manifolds
Weiping Li
Algebr. Geom. Topol. 4(2): 647-684 (2004). DOI: 10.2140/agt.2004.4.647


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 –graded symplectic Floer cohomology is an integral lifting of the usual Σ(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 Σ(L)–graded Floer cohomology is induced from the ring structure of the cohomology of the Lagrangian sub–manifold via the spectral sequence. Using the –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.


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Weiping Li. "The $\mathbb{Z}$–graded symplectic Floer cohomology of monotone Lagrangian sub-manifolds." Algebr. Geom. Topol. 4 (2) 647 - 684, 2004.


Received: 3 December 2002; Accepted: 9 August 2004; Published: 2004
First available in Project Euclid: 21 December 2017

MathSciNet: MR2100676
Digital Object Identifier: 10.2140/agt.2004.4.647

Primary: 53D40
Secondary: 53D12 , 70H05

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

Rights: Copyright © 2004 Mathematical Sciences Publishers


Vol.4 • No. 2 • 2004
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