Math Papers

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The Gysin exact sequence for S^1-equivariant symplectic homology
joint work with Alexandru Oancea,
Journal of Topology and Analysis 5 (2013) no 4, 361-407.

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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. 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.

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This paper appeared in Journal of Topology and Analysis.

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