We produce a nonpositively curved square complex, X, containing exactly four squares. Its universal cover, X̃ ≅ T4 x T 4, is isomorphic to the product of two 4-valent trees. The group, pi1X, is a lattice in Aut (X̃) but π1X is not virtually a nontrivial product of free groups. There is no such example with fewer than four squares. The main ingredient in our analysis is that X̃ contains an "anti-torus" which is a certain aperiodically tiled plane.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.101884 |
| Date | January 2007 |
| Creators | Janzen, David. |
| 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 Arts (Department of Mathematics and Statistics.) |
| Rights | © David Janzen, 2007 |
| Relation | alephsysno: 002668618, proquestno: AAIMR38454, Theses scanned by UMI/ProQuest. |
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