Dört boyutlu egzotik manifoldlar

This thesis aims to review the existence of a pair of exotic 4-manifolds i.e. a pair of 4-manifolds that are homeomorphic but not diffeomorphic. First, we make a few remarks in algebraic topology, which is followed by introduction to vector bundles and characteristic classes. Next, we introduce the intersection form, a bilinear map defined on the second cohomology group (or second homology group via Poincar\'e Duality) of a closed and oriented 4-manifold. Then, we lay out a sufficient list of invariants for isomorphism of indefinite intersection forms, which eases to prove homeomorphism of closed and oriented 4-manifolds with the help of Freedman's theorem. In the following chapter, we start by presenting necessary concepts in order to define Seiberg-Witten equations, whose solution space modded out by an action turns out to be a diffeomorphism invariant for certain smooth 4-manifolds. Finally, we review the construction of two 4-manifolds, and show that they are homeomorphic by Freedman's theorem but not diffeomorphic using their Seiberg-Witten invariants.