# Braid Group Representations and Orbifoldization

Specialeforsvar: Jiahe Cai

TItel: Braid Group Representations and Orbifoldization

Abstract: Let G be a finite group. By evaluation of a once-extended 3-2-1-dimensional Gequivariant topological field theory Z on the circle one obtains a G-ribbon category C. From a homotopy G-fixed point in this G-ribbon category C, we can construct two representations of framed braid groups fBn with n strands for any n ≥ 1). We can construct a representation of fBn by evaluation Z on genus zero surfaces. 2) We can orbifoldize the G-ribbon category C and obtain the fBn representation algebraically by using the braiding and twist of the orbifold category. We prove that these two representations are equivalent.

Vejleder: Lukas Woike
Censor:    Sune Nikolaj Prech Reeh, Netcompany IT