Black holes in the Dynnikov Coordinate Plane

Ferihe Atalan

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arXiv · 2501.07287

Black holes in the Dynnikov Coordinate Plane

Ferihe Atalan

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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 $\mathbb{Z}^{2}$-automorphism preserving the shape of the linearity border fan.

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Ferihe Atalan. 2025-01-13. Black holes in the Dynnikov Coordinate Plane. https://arxiv.org/abs/2501.07287

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