A presentation for the baseleaf preserving mapping class group of the punctured solenoid

We give a presentation for the baseleaf preserving mapping class group $Mod(\S)$ of the punctured solenoid $\S$. The generators for our presentation were introduced previously, and several relations among them were derived. In addition, we show that $Mod(\S)$ has no non-trivial central elements. Our main tool is a new complex of triangulations of the disk upon which $Mod(\S)$ acts.