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arXiv · 0909.4526

The Gysin exact sequence for $S^1$-equivariant symplectic homology

Frédéric Bourgeois·Alexandru Oancea
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Abstract

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.

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Frédéric Bourgeois, Alexandru Oancea. 2009-09-24. The Gysin exact sequence for $S^1$-equivariant symplectic homology. https://arxiv.org/abs/0909.4526

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