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

Abstract

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