Title page for ETD etd-05122008-202129

Type of Document Master's Thesis
Author Ackermann, Robert James
Author's Email Address rackrmnn@vt.edu
URN etd-05122008-202129
Title Constructing Bitwisted Face Pairing 3-Manifolds
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Floyd, William J. Committee Chair
Brown, Ezra A. Committee Member
Thomson, James E. Committee Member
  • Bitwisted 3-manifolds
  • Twisted 3-manifolds
  • Dehn Surgery
  • face pairings
Date of Defense 2008-04-29
Availability unrestricted
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.
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