School Seminars and Colloquia

Thompson's group F and its remarkable Cayley graph

Geometry/Topology Seminar

by Sean Cleary


Institution: City College of New York
Date: Mon 24th April 2006
Time: 3:15 PM
Location: Gypsum Theatre (room 303), Architecture Building

Abstract: In the early 1960's Richard J. Thompson discovered a fascinating family of
finitely-presented groups in connection with his work in logic. These
groups have reappeared in a wide variety of settings, including homotopy
theory, measure theory of discrete groups, non-associative algebras,
dynamical systems and geometric group theory. Thompson's group F is the
simplest known example of a variety of perplexing group-theoretic
phenomena and has been the subject of a great deal of study. I will
describe this group from several different perspectives and discuss some
of its remarkable bizarre properties. The standard Cayley graph of
Thompson's group F has a number of pathological properties, including
dead-end elements, seesaw elements, and highly nonconvex metric balls.

For More Information: Lawrence Reeves email: l.reeves@ms.unimelb.edu.au