## Abstract

In [8,5], the first author and his collaborators constructed the irreducible symplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n-1)CP^{2}#(2n-1)CP^{2} for each integer n≥ 25, and the families of simply connected irreducible nonspin symplectic 4-manifolds with positive signature that are interesting with respect to the symplectic geography problem. In this paper, we improve the main results in [8,5]. In particular, we construct (i) an infinitely many irreducible symplectic and nonsymplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n-1)CP^{2}#(2n-1)CP^{2} for each integer n≥ 12, and (ii) the families of simply connected irreducible nonspin symplectic 4-manifolds that have the smallest Euler characteristics among the all known simply connected 4-manifolds with positive signature and with more than one smooth structure. Our construction uses the complex surfaces of Hirzebruch and Bauer-Catanese on Bogomolov-Miyaoka-Yau line with c_{1}^{2}=9χ_{h}=45, along with the exotic symplectic 4-manifolds constructed in [2,6,4,7,11].

Original language | English (US) |
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Pages (from-to) | 24-45 |

Number of pages | 22 |

Journal | Topology and its Applications |

Volume | 206 |

DOIs | |

State | Published - Jun 15 2016 |

### Bibliographical note

Funding Information:The first author would like to thank Professor Fabrizio Catanese for a useful email exchange on surfaces in [14] . The authors would like to thank the anonymous referee for the valuable comments on the previous version of this manuscript. A. Akhmedov was partially supported by NSF grants DMS-1065955 , DMS-1005741 and Sloan Research Fellowship . S. Sakallı was partially supported by NSF grants DMS-1065955 .

## Keywords

- 4-Manifolds
- Exotic 4-manifolds
- Geography of symplectic 4-manifolds