# An irrational slope Thompson's group

## Seminar/Forum

107
Peter Hall
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.