, Volume 181, Issue 3, pp 577-603
Date: 12 May 2010

Exotic smooth structures on small 4-manifolds with odd signatures

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


Let M be \((2n-1)\mathbb{CP}^{2}\#2n\overline{\mathbb{CP}}{}^{2}\) 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 \(\mathbb{CP}{}^{2}\#4\overline {\mathbb{CP}}{}^{2}\) or \(3\mathbb{CP}{}^{2}\#k\overline{\mathbb{CP}}{}^{2}\) for k=6,8,10.