Year: 2010
Type: preprint
Abstract: We prove an analogue of Farb-Masur's theorem that the length-spectra metric on moduli space is "almost isometric" to a simple model $\mathcal {V}(S)$ which is induced by the cone metric over the complex of curves. As an application, we know that the Teichmüller metric and the length-spectra metric are "almost isometric" on moduli space, while they are not even quasi-isometric on Teichmüller space.
Source: arXiv (Cornell University)
Authors: Liu, Lixin, Su, Weixu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W122009192