Connectivity Bounds and S-Partitions for Triangulated Manifolds

Author

Alexandru Ilarian Papiu, Washington University in St. LouisFollow

Date of Award

Spring 5-15-2017

Author's School

Graduate School of Arts and Sciences

Author's Department

Mathematics

Degree Name

Doctor of Philosophy (PhD)

Degree Type

Dissertation

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.

Language

English (en)

Chair and Committee

John Shareshian

Committee Members

Rachel Roberts, Renato Feres, David Wright, Michael Ogilvie,

Comments

Permanent URL: https://doi.org/10.7936/K7DB8081

Recommended Citation

Papiu, Alexandru Ilarian, "Connectivity Bounds and S-Partitions for Triangulated Manifolds" (2017). Arts & Sciences Electronic Theses and Dissertations. 1137.
https://openscholarship.wustl.edu/art_sci_etds/1137