Cubulating one-relator groups with torsion

• Main Author: Lauer, Joseph.
• Format: Others
• Language: en
• Published: McGill University 2007
• Subjects: Trees (Graph theory); Group theory.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101861

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.