Let <a1,..., a m | wn> be a presentation of a group G, where w is freely and cyclically reduced and n ≥ 2 is maximal. We define a system of codimension-1 subspaces in the universal cover, and invoke a construction essentially due to Sageev to define an action of G on a CAT(0) cube complex. By proving easily formulated geometric properties of the codimension-1 subspaces we show that when n ≥ 4 the action is proper and cocompact, and that the cube complex is finite dimensional and locally finite. We also prove partial results when n = 2 or n = 3. It is also shown that the subgroups of G generated by non-empty proper subsets of {a1, a 2,..., am} embed by isometries into the whole group.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.101861 |
| Date | January 2007 |
| Creators | Lauer, Joseph. |
| 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 | © Joseph Lauer, 2007 |
| Relation | alephsysno: 002666941, proquestno: AAIMR38412, Theses scanned by UMI/ProQuest. |
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