Abstract
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.
Committee Chair
John Shareshian
Committee Members
Rachel Roberts, Renato Feres, David Wright, Michael Ogilvie,
Degree
Doctor of Philosophy (PhD)
Author's Department
Mathematics
Document Type
Dissertation
Date of Award
Spring 5-15-2017
Language
English (en)
DOI
https://doi.org/10.7936/K7DB8081
Recommended Citation
Papiu, Alexandru Ilarian, "Connectivity Bounds and S-Partitions for Triangulated Manifolds" (2017). Arts & Sciences Theses and Dissertations. 1137.
The definitive version is available at https://doi.org/10.7936/K7DB8081
Comments
Permanent URL: https://doi.org/10.7936/K7DB8081