Construction of New Exotic Symplectic 4-Manifolds and Fillings of Contact 3-Manifolds

Abstract

This dissertation studies the geography problem for symplectic/non-symplectic 4-manifolds. Examples of new families of 4-manifolds that is homeomorphic but not diffeomorphic to (2n+2k-3)ℂℙ²#(6n+2k-3)\overline{ℂℙ}², for any n≠1, k≠1, and (n,k) ≠(1,1), are constructed using higher genus Lefschetz fibrations introduced by Yusuf Gürtaş, product 4-manifolds and certain symplectic operations such as Luttinger surgery and symplectic connected sum. As well as, examples of the families of Lefschetz fibrations over S² are discussed which are obtained by using the cyclic group actions on product manifolds. The latter symplectic 4-manifolds has nice applications using rational blow-down and equivariant sum.