A NEW CONSTRUCTION OF SYMPLECTIC-MANIFOLDS

• 成果类型: Article
• 署名作者: GOMPF, RE
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2118554
• 发表日期: 1995
• 页码: 527-595
• 关键词: elliptic-surfaces; general type; 4-manifolds; INVARIANTS; TOPOLOGY; Examples; complex

摘要

In each even dimension greater than or equal to 4, families of compact, symplectic manifolds are constructed, such that all finitely presentable groups occur as fundamental groups. For each group, these manifolds can be assumed not to be homotopy equivalent to Kahler manifolds. Other examples are constructed that are homeomorphic, but not diffeomorphic, to simply connected, Kahler surfaces. The geography of compact, symplectic 4-manifolds is studied, with a result that for any fixed fundamental group, it is possible to realize any value of the first Chern number c(1)(2) or the signature. Explicit results are obtained about simultaneously realizing both Chern numbers (or equivalently, the signature and Euler characteristic), for any fixed fundamental group. Various other applications are presented.