Loft, Brian2018-04-262018-04-262018-052018-04-12May 2018http://hdl.handle.net/20.500.11875/2353In 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.application/pdfenDifferential GeometrySmooth Morse TheoryDiscrete Morse TheorySurgeryCobordismCellular SurgeryLocally Cellular Cobordant.Thesis2018-04-26