Finding geodesics in a triangulated 2-sphere

Abigail Thompson

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arXiv · 1408.5949

Finding geodesics in a triangulated 2-sphere

Abigail Thompson

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Abstract

Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be unstable, corresponding, for example, to the three equators of an ellipsoid. Using a piece-wise linear approach, we show that we can usually find at least three stable geodesics.

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Abigail Thompson. 2014-08-25. Finding geodesics in a triangulated 2-sphere. https://arxiv.org/abs/1408.5949

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