Exotic smooth structures on small 4-manifolds with odd signatures

• 成果类型: Article
• 署名作者: Akhmedov, Anar; Park, B. Doug
• 署名单位: University of Waterloo; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0254-y
• 发表日期: 2010
• 页码: 577-603
• 关键词: symplectic 4-manifolds; lagrangian tori; SURFACES; TOPOLOGY

摘要

Let M be (2n - 1)CP2#2n (CP) over bar (2) for any integer n >= 1. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structures when M is CP2#4 (CP) over bar (2) or 3CP(2)#k (CP) over bar (2) for k = 6, 8 10.