Anar Akhmedov

EXOTIC SMOOTH STRUCTURES ON SMALL 4-MANIFOLDS WITH ODD SIGNATURES

Let M be

Constructing infinitely many smooth structures on small 4-manifolds

(2n-1)\mathbb{CP}^{2}\#2n\overline{\mathbb{CP}}{}^{2}

Exotic smooth structures on small 4-manifolds

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

Simply connected minimal symplectic 4-manifolds with signature less than - 1

\mathbb{CP}{}^{2}\#4\overline {\mathbb{CP}}{}^{2}

Small exotic 4-manifolds

or

Exotic Stein fillings with arbitrary fundamental group

3\mathbb{CP}{}^{2}\#k\overline{\mathbb{CP}}{}^{2}

Singularity links with exotic stein fillings

for k=6,8,10.

New exotic 4-manifolds via Luttinger surgery on Lefschetz fibrations

The purpose of this article is twofold. First we outline a general construction scheme for producing simply-connected minimal symplectic 4-manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain irreducible symplectic 4-manifolds homeomorphic but not diffeomorphic to

Constructing Lefschetz fibrations via daisy substitutions

\CP#(2k+1)\CPb

Lantern substitution and new symplectic 4-manifolds with

for