The level four braid group

Brendle, T. E. and Margalit, D. (2018) The level four braid group. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 735, pp. 249-264. (doi: 10.1515/crelle-2015-0032)

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By evaluating the Burau representation at t=-1, we obtain a symplectic representation of the braid group. We study the resulting congruence subgroups of the braid group, namely, the preimages of the principal congruence subgroups of the symplectic group. Our main result is that the level 4 congruence subgroup is equal to the group generated by squares of Dehn twists. We also show that the image of the Brunnian subgroup of the braid group under the symplectic representation is the level four congruence subgroup.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Brendle, Professor Tara
Authors: Brendle, T. E., and Margalit, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal für die Reine und Angewandte Mathematik (Crelles Journal)
Publisher:Walter de Gruyter
ISSN (Online):1435-5345
Published Online:31 July 2015
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
595131Mapping Class Groups and Related Structures.Tara BrendleEngineering & Physical Sciences Research Council (EPSRC)EP/J019593/1M&S - MATHEMATICS