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arXiv · 0704.2169

An exact sequence for contact- and symplectic homology

Frédéric Bourgeois·Alexandru Oancea
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Abstract

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.

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Frédéric Bourgeois, Alexandru Oancea. 2008-10-15. An exact sequence for contact- and symplectic homology. https://doi.org/10.1007/s00222-008-0159-1

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