Event Type:

Ph.D.Defense

Date/Time:

Wednesday, June 14, 2017 - 12:00 to 14:00

Location:

Valley Library Willamette West Room

Abstract:

Groups given by generators and relations are naturally related to topology via the fundamental group. Indeed, given a group presentation one can form a two dimensional cellular model whose fundamental group is given by the presentation. We may therefore speak of topological properties of a group presentation, where it is well known that topological properties of the model influence the structure of the group. This dissertation investigates the group structure and topological properties of cyclically presented groups. A group with a cyclically symmetric presentation admits an automorphism of finite order call the shift. The main results include the construction of a family of 3-manifolds with cyclically presented spines, obtained from centrally extended triangle groups; the classification of the shift dynamics of two families of cyclically presented groups, exhibiting a wide variety of properties; and an investigation into the structure of cyclic presentations with composite relations, leading to the construction of a family of higher dimensional knot groups.

Kirk's major professor is Prof. Bill Bogley.