Special Lecture: Sonja Mitchel (UCSB), 'A Type B Version of Thompson's Group F'

Event Date: 

Tuesday, July 23, 2013 -
1:00pm to 2:00pm

Event Location: 

  • 6635 South Hall

Event Contact: 

Sonja Mitchell

Email: smitchell@math.ucsb.edu

ABSTRACT:

Thompson's Group F is a finitely presented infinite group which has proved a rich source of counterexamples for group theorists. We re-consider the group as represented by polygons in the Farey triangulation of the
hyperbolic plane. Through this lens, the group is linked to the associahedra, an infinite family of convex polytopes. By analogy with the type B associahedra, known as the cyclohedra, we define a type B version
of Thompson's Group F, show that this group is contained in Thompson's Group T, and give finite and infinite presentations and normal forms of F_B by utilizing a quotient of the group which is isomorphic to T.