A divergent horocycle in the horofunction compactification of the Teichmüller metric

2019/11/23 by Bourque, Maxime Fortier
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1911.10365

Abstract

We give an example of a horocycle in the Teichmüller space of the five-times-punctured sphere that does not converge in the Gardiner--Masur compactification, or equivalently in the horofunction compactification of the Teichmüller 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 Teichmüller space of complex dimension greater than one via covering constructions.

Related

• The horofunction compactification of Teichmüller metric
• Convergence of earthquake and horocycle paths to the boundary of Teichmüller space
• A horofunction counterpart to Teichmüller distance
• The asymptotic geometry of the Teichmüller metric
• Convergence of some horocyclic deformations to the Gardiner-Masur\n boundary