Advisory Committee Chair
Mubenga N Nkashama
Advisory Committee Members
Ian W Knowles
Date of Award
Degree Name by School
Master of Science (MS) College of Arts and Sciences
Morse Theory is a subset of manifold theory that looks at non-degenerate critical points of functions on manifolds. The Morse Lemma allows for a local coordinate system to be made around a non-degenerate critical point to express the function in a standard form. When these properties come together to describe the manifold on a global level it can have significant results related to its various diffeomorphisms. I will discuss some of these unique properties that Morse Theory has in identifying the generalized shape of surfaces, and then expand that into finitely many dimensions. I will show that any smooth function on the manifold can be approximated in some sense by a function where all the critical points are non-degenerate. I will end by discussing the shape and decomposition of handlebodies in m-dimensions.
Tidwell, William Smith, "Morse Theory in Finite Dimensions" (2017). All ETDs from UAB. 3147.