A divergent horocycle in the horofunction compactification of the Teichm\"uller metric

Maxime Fortier Bourque

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arXiv · 1911.10365

A divergent horocycle in the horofunction compactification of the Teichm\"uller metric

Maxime Fortier Bourque

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Abstract

We give an example of a horocycle in the Teichm\"uller space of the five-times-punctured sphere that does not converge in the Gardiner--Masur compactification, or equivalently in the horofunction compactification of the Teichm\"uller metric. As an intermediate step, we exhibit a simple closed curve whose extremal length is periodic but not constant along the horocycle. The example lifts to any Teichm\"uller space of complex dimension greater than one via covering constructions.

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Maxime Fortier Bourque. 2019-11-23. A divergent horocycle in the horofunction compactification of the Teichm\"uller metric. https://arxiv.org/abs/1911.10365

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