#### Volume 7, issue 3 (2007)

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

### Sylvain Bonnot, Robert C Penner and Dragomir Šarić

Algebraic & Geometric Topology 7 (2007) 1171–1199
 arXiv: math.DS/0608066
##### Abstract

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

##### Keywords
solenoid, punctured solenoid, baseleaf preserving mapping class group, Whitehead move, presentation, triangulation complex
Primary: 57M99
Secondary: 20F65