Constructing Bitwisted Face Pairing 3-Manifolds

The bitwist construction, originally discovered by Cannon, Floyd, and Parry, gives us a new method for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a link without changing the topology of the manifold obtained by Dehn Surgery. Once the theory has been developed, I will apply it to find several bitwist representations of the Poincaré Sphere and 3-Torus. Finally, I discuss how one might attempt to find a set of moves that can take one bitwist representation of a manifold to any other bitwist representation of the same manifold.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2008

Author dc:creator

• Ackermann, Robert James

Chair dc:contributor.committeechair

• Floyd, William J.

Committee members dc:contributor.committeemember

• Thomson, James E.
• Brown, Ezra A.

• Bitwisted 3-manifolds
• Twisted 3-manifolds
• Dehn Surgery
• face pairings

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05122008-202129

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32655