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,

Comments

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

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Spring 5-15-2017

Language

English (en)

Included in

Mathematics Commons

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