Mathematics – Symplectic Geometry
Scientific paper
2009-09-24
Mathematics
Symplectic Geometry
67 pages
Scientific paper
We define $S^1$-equivariant symplectic homology for symplectically aspherical manifolds with contact boundary, using a Floer-type construction first proposed by Viterbo. We show that it is related to the usual symplectic homology by a Gysin exact sequence. As an important ingredient of the proof, we define a parametrized version of symplectic homology, corresponding to families of Hamiltonian functions indexed by a finite dimensional smooth parameter space. We define a parametrized version of the Robbin-Salamon index, which gives the grading for these new versions of symplectic homology. We indicate several applications and ramifications of our constructions.
Bourgeois Frédéric
Oancea Alexandru
No associations
LandOfFree
The Gysin exact sequence for $S^1$-equivariant symplectic homology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Gysin exact sequence for $S^1$-equivariant symplectic homology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Gysin exact sequence for $S^1$-equivariant symplectic homology will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-425801