4-boyutlu pürüzsüz manifoldlarin kulp dagilimlari üzerine

The topology of manifold theory relates to many diverse fields of mathematics such as abstract algebra, differential and algebraic geometry, and analysis. Therefore there are many approaches to manifold theory among mathematicians. Our study based on topological viewpoint relating algebraic topology and geometric topology. In this thesis, we study handlebodies of 4-dimensional closed connected smooth manifolds. In order to work with smooth handles we use handle operations. These operations are basically handle sliding, handle cancelling and carving. Then by using these operations we investigate Gluck twisting. 4-dimensional smooth manifolds has its own significance among other manifolds, its importance is related to the classification problem. All techniques that are used in this thesis historically have been developed over the years to classify smooth 4-dimensional manifolds. Keywords: Four dimensional smooth manifolds, handlebody, handle sliding, handle cancelling, carving, Gluck twist.