Künneth formulae and cross products for the symplectic Floer cohomology
✍ Scribed by Weiping Li
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 231 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0166-8641
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✦ Synopsis
For a symplectic monotone manifold (P , ω) and φ ∈ Symp 0 (P , ω), we define a Z-graded symplectic Floer cohomology (a local invariant) over integral coefficients. There is a spectral sequence which arises from a filtration on the Z-graded symplectic Floer cochain complex. The spectral sequence converges to the Z 2N -graded symplectic Floer cohomology (a global invariant). We show that there are cross products on the Z-graded symplectic Floer cohomology and on the spectral sequence, hence on the usual Z 2N -graded symplectic Floer cohomology. The Künneth formula for the Z-graded symplectic Floer cohomology is proved and similar results for the spectral sequence are obtained.