The intrinsic asymmetry and inhomogeneity of Teichmuller space

Benson Farb; Shmuel Weinberger

doi:10.1215/00127094-2010-051

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arXiv · 0804.4428

The intrinsic asymmetry and inhomogeneity of Teichmuller space

Benson Farb·Shmuel Weinberger

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Abstract

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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Benson Farb, Shmuel Weinberger. 2008-04-28. The intrinsic asymmetry and inhomogeneity of Teichmuller space. https://doi.org/10.1215/00127094-2010-051

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