Browsing Theses and Dissertations by Author "Xia, Jingfeng"
GT-shadows related to finite quotients of the full modular groupDolgushev, Vasily; Lorenz, Martin, 1951-; Stover, Matthew; Combe, Noémie (Temple University. Libraries, 2021)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 . GT-shadows  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.