Tekil uzaylar için Morse teorisi

In this thesis, our aim is to understand Morse Theory for singular spaces. To reach this aim, we have studied the Classical Morse Theory which follows from the book of Yukio Matsumoto "An Introduction to Morse Theory". We have considered some theorems of Morse Theory for compact smooth manifolds without boundary and try to understand the proofs of these theorems. Furthermore, we have studied on Whitney stratification of a topological space using the transversality property of the strata.Afterwards, we have tried to understand how Whitney stratification divides topological spaces and also singular spaces into strata which are smooth submanifolds.Finally, we have examined the Morse theory for singular spaces using the Whitney stratification which follows from the book of Goresky and MacPherson "Stratified Morse Theory".Keywords: Non-degenerate critical point, Hessian matrix, index, Morse function, gradient like vector field, handle decomposition, strata, stratification, Whitney stratification, transversality, Morse data, normal and tangential Morse data, singular point, singular space.