Cycle-Free Twisted Face-Pairing 3-Manifolds
| dc.contributor.author | Gartland, Christopher John | en |
| dc.contributor.committeechair | Floyd, William J. | en |
| dc.contributor.committeemember | Linnell, Peter A. | en |
| dc.contributor.committeemember | Haskell, Peter E. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2014-05-30T08:00:54Z | en |
| dc.date.available | 2014-05-30T08:00:54Z | en |
| dc.date.issued | 2014-05-29 | en |
| dc.description.abstract | 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. | en |
| dc.description.degree | Master of Science | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:3082 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/48188 | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | 3-manifolds | en |
| dc.subject | plumbing graphs | en |
| dc.subject | Seifert fibered spaces | en |
| dc.subject | face-pairings | en |
| dc.title | Cycle-Free Twisted Face-Pairing 3-Manifolds | en |
| dc.type | Thesis | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | masters | en |
| thesis.degree.name | Master of Science | en |
Files
Original bundle
1 - 1 of 1