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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 26, Issue 2


Free subgroups within the images of quantum representations

Louis Funar / Toshitake Kohno
  • IPMU, Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-Ku, Tokyo 153-8914, Japan
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Published Online: 2011-11-08 | DOI: https://doi.org/10.1515/form.2011.162


We prove that, except for a few explicit roots of unity, the quantum image of any Johnson subgroup of the mapping class group contains an explicit free non-abelian subgroup.

Keywords: Mapping class group; Dehn twist; triangle group; braid group; Burau representation; Johnson filtration; quantum representation

MSC: 57M07; 20F36; 20F38; 57N05

About the article

Received: 2011-09-23

Revised: 2011-10-24

Published Online: 2011-11-08

Published in Print: 2014-03-01

Funding Source: Grant-in-Aid for Scientific Research (Japan Society for Promotion of Science)

Award identifier / Grant number: 23340014

Funding Source: World Premier International Research Center Initiative

Award identifier / Grant number: MEXT

Citation Information: Forum Mathematicum, Volume 26, Issue 2, Pages 337–355, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.162.

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