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

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/