An exact sequence for contact- and symplectic homology

2007/04/30 by Frédéric Bourgeois, Alexandru Oancea · 1 citation
Mathematics · #math.SG #msc:54D30

paper · pdf · doi:10.1007/s00222-008-0159-1

Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modifications

arxiv created 2008/10/15 · arxiv updated 2015/05/12

Abstract

A symplectic manifold W with contact type boundary M = ∂ 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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