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GT-shadows related to finite quotients of the full modular group

Xia, Jingfeng
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Thesis/Dissertation
Date
2021
Advisor
Dolgushev, Vasily
Committee member
Lorenz, Martin, 1951-
Stover, Matthew
Combe, Noémie
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Department
Subject
Mathematics
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http://hdl.handle.net/20.500.12613/6910
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Xia_temple_0225M_14657.pdf
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DOI
http://dx.doi.org/10.34944/dspace/6892
Abstract
GT-shadows are tantalizing objects that can be thought of as “approximations” to elements of the mysterious Grothendieck-Teichmueller group GT introduced by V. Drinfeld in 1990 [5]. GT-shadows [4] form a groupoid whose objects are certain finite index normal subgroups of Artin’s braid group B4 on 4 strands. In this thesis we introduce GT-shadows for the gentle version GTgen of the Grothendieck-Teichmueller group. These entities are morphisms of a groupoid GTSh whose objects are certain finite index normal subgroups of Artin’s braid group B3 on 3 strands. We explore the connected components of GTSh for sub- groups of B3 coming from the standard homomorphism from B3 to SL2(Z/qZ), where q is a power of an odd prime integer > 3.
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