An exact sequence for contact- and symplectic homology

• 成果类型: Article
• 署名作者: Bourgeois, Frederic; Oancea, Alexandru
• 署名单位: Universite Libre de Bruxelles; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-008-0159-1
• 发表日期: 2009
• 页码: 611-680
• 关键词: floer homology; field-theory; maslov index; Transversality; MANIFOLDS

摘要

A symplectic manifold W with contact type boundary M=a,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.