Groups generated by Dehn twists along fillings of surfaces

Let [Formula: see text] denote a closed oriented surface of genus [Formula: see text]. A set [Formula: see text] of pairwise non-homotopic simple closed curves on [Formula: see text] such that [Formula: see text] and [Formula: see text] are in minimal position, is called a filling system or simply a filling of [Formula: see text], if [Formula: see text] is a disjoint union of [Formula: see text] topological discs for some [Formula: see text]. For [Formula: see text], let [Formula: see text] denote the Dehn twist along [Formula: see text]. In this paper, we show that for each [Formula: see text], there exists a filling [Formula: see text] of [Formula: see text] such that the group [Formula: see text] is isomorphic to the free group of rank [Formula: see text].