The Gysin exact sequence for S¹-equivariant symplectic homology

2009/09/30 by Frédéric Bourgeois, Alexandru Oancea · 2 citations
Mathematics · #math.SG #math.AT #msc:53D40 #msc:55P50 #msc:53D12

paper · pdf

published as J. Topol. Anal. 5 (2013), no. 5, 361-407 · v3: 48 pages. Added Lemma 5.8 relating the long exact sequence of the cone and the Gysin sequence. Various other modifications throughout the text following referee's comments. This is the final version published in J. Topol. Anal

arxiv created 2013/12/20 · arxiv updated 2013/12/23

Abstract

We define S¹-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.

Cited by

• Filtered Symplectic Homology and Closed Reeb Orbits
• Closed Reeb orbits on contact type hypersurfaces in T^*Sⁿ

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• S¹-equivariant symplectic homology and linearized contact homology
• An exact sequence for contact- and symplectic homology
• A symplectic Gysin sequence
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