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

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.

Grantor dc:publisher

Temple University. Libraries

Year dc:date.issued

2021

Author dc:creator

• Xia, Jingfeng

Advisor dc:contributor.advisor

• Dolgushev, Vasily

Committee members dc:contributor.committeemember

• Lorenz, Martin, 1951-
• Stover, Matthew
• Combe, Noémie

• Mathematics

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Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/20.500.12613/6910

OAI identifier oai:identifier

oai:scholarshare.temple.edu:20.500.12613/6910