Akademik Veri Yönetim Sistemi
Arxiv, cilt.1, sa.1, ss.1-10, 2025 (Hakemsiz Dergi)
We prove that Dehn twists about opposite curves that define a complete partition on an $n$-punctured disk $D_n$ generate either a free group or a free product of abelian groups. Additionally, we introduce an algorithm based on Dynnikov coordinates to determine whether a given collection of opposite curves forms a complete partition. This algorithm not only verifies completeness but also reveals the exact structure of the free products generated by these Dehn twists, relying solely on the Dynnikov coordinates of the curves as input.