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Cubulating one-relator groups with torsion

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.

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.101861
Date January 2007
CreatorsLauer, Joseph.
PublisherMcGill University
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Formatapplication/pdf
CoverageMaster of Science (Department of Mathematics and Statistics.)
Rights© Joseph Lauer, 2007
Relationalephsysno: 002666941, proquestno: AAIMR38412, Theses scanned by UMI/ProQuest.

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