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

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

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Keywords

solenoid, punctured solenoid, baseleaf preserving mapping class group, Whitehead move, presentation, triangulation complex

Mathematical Subject Classification 2000

Primary: 57M99

Secondary: 20F65

References

Publication

Received: 6 November 2006

Revised: 29 June 2007

Published: 24 September 2007

Authors

Sylvain Bonnot
Institute for Mathematical Sciences Stony Brook University Stony Brook NY 11794-3660
http://www.math.sunysb.edu/~bonnot/
Robert C Penner
Departments of Mathematics and Physics/Astronomy University of Southern California Los Angeles CA 90089
http://www-rcf.usc.edu/~rpenner/
Dragomir Šarić
Institute for Mathematical Sciences Stony Brook University Stony Brook NY 11794-3660 Current address: Department of Mathematics Queens College of CUNY 65-30 Kissena Blvd Flushing NY 11367
http://www.math.sunysb.edu/~saric/

Volume 7, issue 3 (2007)

Sylvain Bonnot, Robert C Penner and Dragomir Šarić

Abstract