Date of Award
Doctor of Philosophy (PhD)
Two of the fundamental results in the theory of convex polytopes are Balinski’s Theorem on connectivity and Bruggesser and Mani’s theorem on shellability. Here we present results that attempt to generalize both results to triangulated manifolds. We obtain new connectivity bounds for complexes with certain missing faces and introduce a way to measure how far a manifold is from being shellable using S-partitions and the Stanley-Reisner Ring.
Chair and Committee
Rachel Roberts, Renato Feres, David Wright, Michael Ogilvie,
Papiu, Alexandru Ilarian, "Connectivity Bounds and S-Partitions for Triangulated Manifolds" (2017). Arts & Sciences Electronic Theses and Dissertations. 1137.