Dynnikov coordinates and 𝜋1 −train tracks

The aim of this thesis is to introduce transition formulae between Dynnikov coordinates and π_1-train track coordinates of multi curves on the n-punctured disk D_n. Dynnikov's coordinate system gives an explicit bijection between the set of multi curvess L_n and Ζ^({2n-4})\\{0} on D_n. An alternative way to coordinatize multi curves is achieved by π_1-train track coordinates. This thesis gives transition formulae between Dynnikov coordinates and π_1-train track coordinates of multi curves. This provides a way to compute the geometric intersection number of two multi curves on D_n in terms of π_1-train track coordinates.