In 2-dimensional topology, quotients of polygons by edge-pairings provide a rich source of examples of closed, connected, orientable surfaces. In fact, they provide all such examples. The 3-dimensional analogue of an edge-pairing of a polygon is a face-pairing of a faceted 3-ball. Unfortunately, quotients of faceted 3-balls by face-pairings rarely provide us with examples of 3-manifolds due to singularities that arise at the vertices. However, any face-pairing of a faceted 3-ball may be slighted modified so that its quotient is a genuine manifold, i.e. free of singularities. The modified face-pairing is called a twisted face-pairing. It is natural to ask which closed, connected, orientable 3-manifolds may be obtained as quotients of twisted face-pairings. In this paper, we focus on a special class of face-pairings called cycle-free twisted face-pairings and give description of their quotient spaces in terms of integer weighted graphs. We use this description to prove that most spherical 3-manifolds can be obtained as quotients of cycle-free twisted face-pairings, but the Poincaré homology 3-sphere cannot. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/48188 |
| Date | 29 May 2014 |
| Creators | Gartland, Christopher John |
| Contributors | Mathematics, Floyd, William J., Linnell, Peter A., Haskell, Peter E. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
Page generated in 0.1658 seconds