Generating the Free Group of Rank Two with Dynnikov Coordinates
Abstract
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
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References
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Details
Primary Language
English
Subjects
Group Theory and Generalisations , Topology
Journal Section
Research Article
Publication Date
April 29, 2026
Submission Date
January 9, 2026
Acceptance Date
April 2, 2026
Published in Issue
Year 2026 Volume: 47 Number: 2