The September 22, 2014 O.M.N.I. Talk: Matthew Clay presents

Thompson's group F

Abstract: Thompson's group F is the subgroup of orientation preserving piecewise linear homeomorphisms of [0,1] whose slopes are all powers of 2 and whose breakpoints are rational numbers whose denominators are powers of 2. This group has many interesting properties, for instance it contains a subgroup that is isomorphic to the infinite direct product F x F x F ... . It is also a potential counterexample to a pair of open questions in group theory. We will look at Thompson's group F and some of these interesting properties.