| In the 1990s Robin Forman carefully generalized Morse theory to cellular complexes. In this thesis we are concerned with the connection Morse theory provides in surgery theory. There exists a theorem linking surgery on embedded spheres to cobordisms whose proof relies on smooth Morse theory. Therefore, we examine if a similar theorem exists on cellular complexes whose proof relies on discrete Morse theory. In order to accomplish this we will provide a way to perform surgery on cellular complexes as well as a possibility for defining cellular cobordism. |
