Document Type

Dissertation

Date of Degree

Spring 2017

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Maggy Tomova

Abstract

A closed, orientable, splitting surface in an oriented 3-manifold is a topologically minimal surface of index n if its associated disk complex is (n-2)-connected but not (n-1)-connected. A critical surface is a topologically minimal surface of index 2. In this thesis, we use an equivalent combinatorial definition of critical surfaces to construct the first known critical bridge spheres for nontrivial links.

Keywords

Bridge sphere, Critical, Link, Plat position, Topologically minimal

Pages

vii, 52 pages

Bibliography

Includes bibliographical references (page 52).

Copyright

Copyright © 2017 Daniel Rodman

Included in

Mathematics Commons

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