LGRT 1681
Created by Manin, modular symbols are classes of paths on Q U {\infty}: elements of the relative homology group H_1(X, cusps) where X is the modular curve, the quotient of a congruence subgroup of SL_2(Z) on the complex upper half plane. He was able to find the explicit generators for this group as well as the complete set of relations. Later, Teitelbaum constructed modular symbols over the rational function field F_q(T). He was able to define modular symbols and the complete set of relations for this case, which we will explore in this talk. But we will first construct the analogs of the complex upper half plane, SL_2(Z), and the modular curve X. In the remaining time, I will talk about my current research, which builds off of his work.