A construction of minimal coherent filling pairs

Let denote the genus g closed orientable surface. A coherent filling pair of simple closed curves, in, is a filling pair that has its geometric intersection number equal to the absolute value of its algebraic intersection number. A minimally intersecting filling pair, in, is one whose intersection number is the minimal among all filling pairs of. In this paper, we give a simple geometric procedure for constructing minimally intersecting coherent filling pairs on from the starting point of a coherent filling pair of curves on a torus. Coherent filling pairs have a natural correspondence to square-tiled surfaces, or origamis, and we discuss the origami obtained from the construction.