Date of Award

5-2024

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Trapp, Rolland

Abstract

In this thesis, we will look at finding bounds for the Cheeger constant of links. We will do this by analyzing an infinite family of links call two-bridge fully augmented links. In order to find a bound on the Cheeger constant, we will look for the Cheeger constant of the link’s crushtacean. We will use that Cheeger constant to give us insight on a good cut for the link itself, and use that cut to obtain a bound. This method gives us a constructive way to find an upper bound on the Cheeger constant of a two-bridge fully augmented link. With this method, we will also make a conjecture on the upper bound of any link.

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