Detecting Free Products in the Mapping Class Group of Punctured Disks via Dynnikov Coordinates

Elif Medetoğulları, Elif Dalyan, S. Öykü Yurttaş

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. Ad…