The intrinsic asymmetry and inhomogeneity of Teichmuller space

Details The intrinsic asymmetry and inhomogeneity of Teichmuller space The intrinsic asymmetry and inhomogeneity of Teichmuller space

2008-04-28

arxiv.org/abs/0804.4428v2

Mathematics

Geometric Topology

11 pages, major revisions. To appear in Duke Math Jour

Scientific paper

Royden proved that any isometry of Teichmuller space in the Teichmuller metric must be an element of the extended mapping class group M(S). He also proved that the Teichmuller metric is not symmetric at any point. In this paper we give extensions of Royden's theorems from the Teichmuller metric to an arbitrary complete, finite covolume, M(S)-invariant Finsler (e.g. Riemannian) metric on Teichmuller space. In particular this gives a new mechanism behind Royden's original theorem.

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