We define the notion of relative sectional curvature for 2-complexes, and prove that a compact angled 2-complex that has negative sectional curvature relative to planar sections has coherent fundamental group. We analyze a certain type of 1-complex that we call flattenable graphs Gamma→ X for an compact angled 2-complex X, and show that if X has nonpositive sectional curvature, and if for every flattenable graph pi1 (Gamma) → pi1( X) is finitely presented, then X has coherent fundamental group. Finally we show that if X is a compact angled 2-complex with negative sectional curvature relative to pi-gons and planar sections then pi1(X) is coherent. Some results are provided which are useful for creating examples of 2-complexes with these properties, or to test a 2-complex for these properties.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.111589 |
| Date | January 2009 |
| Creators | Requeima, James. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Mathematics and Statistics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 003164462, proquestno: AAIMR66892, Theses scanned by UMI/ProQuest. |
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