Black holes in the Dynnikov Coordinate Plane

2025/01/13 by Atalan, Ferihe
#37E30 #57K20 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2501.07287

Abstract

This work presents an application of Dynnikov coordinates in geometric group theory. We describe the orbits and dynamics of the action of Dehn twists t_c and t_d in the Dynnikov coordinate plane for a thrice-punctured disc M, where c and d are simple closed curves with Dynnikov coordinates (0,1) and (0,-1), respectively. This action has an interesting geometric meaning as a piecewise linear ℤ²-automorphism preserving the shape of the linearity border fan.

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