Generalized dynnikov coordinates on the finitely punctured torus

In this thesis, we generalize the Dynnikov coordinate system on the finitely punctured disk to an orientable surface Sn of genus 1 with n (n ≥ 2) punctures and 1 boundary component. In particular, we introduce the generalized Dynnikov coordinate system which gives a bijection from the set of integral laminations on Sn to Z^(2n+2)\Vn where Vn = {(a;b;T;c): c ≤ 0 ve T ≠ 0}∪{0}, which can also be generalized to the set of measured foliations on Sn. Keywords: Integral Lamination, Geometric Intersection Number, Generalized Dynnikov Coordinates.