High-distance splittings of 3-manifolds
| dc.contributor.advisor | Hempel, John | en_US |
| dc.creator | Marinenko, Tatiana | en_US |
| dc.date.accessioned | 2009-06-04T08:11:04Z | en_US |
| dc.date.available | 2009-06-04T08:11:04Z | en_US |
| dc.date.issued | 2003 | en_US |
| dc.description.abstract | A Heegaard splitting (S; V1, V 2) for a closed 3-manifold M is a representation M = V1 ∪S V2 where V1 and V 2 are handlebodies and S = ∂V 1 = ∂V2 = V 1 ∩ V2. The distance of a Heegaard splitting (S; V1, V2) is the length of a shortest path in the curve complex of S which connects the subcomplexes KV1 and KV2 , where KVi is the subcomplex consisting of all vertices that correspond to simple closed curves bounding disks in Vi for i = 1, 2. In this work we explicitly define an infinite sequence of 3-manifolds {Mn} via their representative Heegaard diagrams by iterating a 2-fold Dehn twist operator. Using purely combinatorial techniques we are able to prove that for any n the distance of the Heegaard Splitting of Mn is at least n. Moreover, we show that pi1(Mn) surjects onto pi1(Mn-1 ). Hence, if we assume that M0 has a non-trivial boundary, i.e. first Betti number beta1( M0) > 0, then it follows that beta1( Mn) > 0 for all n ≥ 1. Therefore, the sequence {Mn} consists of Haken 3-manifolds for n ≥ 1 and hyperbolizable 3-manifolds for n ≥ 3. | en_US |
| dc.format.extent | 50 p. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.callno | THESIS MATH. 2003 MARINENKO | en_US |
| dc.identifier.citation | Marinenko, Tatiana. "High-distance splittings of 3-manifolds." (2003) Diss., Rice University. <a href="https://hdl.handle.net/1911/18553">https://hdl.handle.net/1911/18553</a>. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/18553 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | en_US |
| dc.subject | Mathematics | en_US |
| dc.title | High-distance splittings of 3-manifolds | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Mathematics | en_US |
| thesis.degree.discipline | Natural Sciences | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.name | Doctor of Philosophy | en_US |
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