The horoboundary and isometry group of Thurston's Lipschitz metric

Cormac Walsh

The horoboundary and isometry group of Thurston's Lipschitz metric

Geometric Topology 2015-10-05 v4 Metric Geometry

Authors: Cormac Walsh

Abstract

We show that the horofunction boundary of Teichm\"uller space with Thurston's Lipschitz metric is the same as the Thurston boundary. We use this to determine the isometry group of the Lipschitz metric, apart from in some exceptional cases. We also show that the Teichm\"uller spaces of different surfaces, when endowed with this metric, are not isometric, again with some possible exceptions of low genus.

Keywords

horoboundary Thurston boundary Teichmüller space Lipschitz metric isometry group moduli space

Cite

@article{arxiv.1006.2158,
  title  = {The horoboundary and isometry group of Thurston's Lipschitz metric},
  author = {Cormac Walsh},
  journal= {arXiv preprint arXiv:1006.2158},
  year   = {2015}
}

Comments

23 pages, 5 figures. There was a mistake in one of the lemmas. Fixing it required replacing Lemmas 7.5, 7.6, and 7.7. The new version is very close to the published version

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