An irrational slope Thompson's group
Thompson's groups were introduced in the 1960s and have since been of much interest to group theorists.
I will discuss a similar group (introduced by Cleary) whose elements are piecewise linear homeomorphisms of \( [0,1]\) having breakpoints
in \(Z[a] \) and slopes a power of \(a\), where a is a root of \( x^2+x-1.\) This group has a structure which is similar to that of Thompson's group \(F\), and shares many of its properties.
Dr Lawrence Reeves, University of Melbourne