Exotic Smooth Structures on Small 4-Manifolds with Odd Signatures

2007/01/29 by Anar Akhmedov, Akhmedov, Anar, B. Doug Park +1
Mathematics · #57R17 #57R55 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0701829

openalex publication_date 2007/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be \CP#2\CPb, 3\CP#4\CPb or (2n-1)\CP#2n\CPb for any integer n≥ 3. 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 \CP#4\CPb or 3\CP# k \CPb for k=6,8,10.

Related

• Exotic 4-manifolds with signature zero
• Small Exotic 4-Manifolds
• Construction of Exotic Smooth Structures
• Exotic Structures on smooth 4-manifolds
• Exotic smooth structures on 3CP²#8-CP²