Word Length Formulae, Normal Forms, Conjugation and Root-finding Algorithms in Surface Groups

Ke Wang, Qiang Zhang, Xuezhi Zhao

In this paper, we mainly study the following symmetric presentation of the surface group $$π_1(Σ_g)=\left\langle c_1,\dots, c_{2g}\mid c_1\cdots c_{2g}c_1^{-1}\cdots c_{2g}^{-1}\ri…