Akademik Veri Yönetim Sistemi
CUMHURIYET SCIENCE JOURNAL, cilt.47, sa.2, ss.356-360, 2026 (TRDizin)
It is well known that if the geometric intersection number of two simple closed curves is at least two, then the Dehn twists about these curves generate a free group of rank two. In this paper, we consider a pair of intersecting standard curves in the three-punctured disk D3 and show that the corresponding Dehn twists generate a free group of rank two. This result is proved using a coordinate-based alternative approach formulated entirely in terms of Dynnikov coordinates, which allows the ping–pong dynamics providing a sufficient criterion for freeness to be seen explicitly.