Weil-Petersson translation distance and volumes of mapping tori

Details Weil-Petersson translation distance and volumes of mapping tori Weil-Petersson translation distance and volumes of mapping tori

2001-09-07

arxiv.org/abs/math/0109050v1

Mathematics

Geometric Topology

10 pages, 2 figures

Scientific paper

Given a closed hyperbolic 3-manifold T_\psi that fibers over the circle with monodromy \psi : S -> S, the monodromy $\psi$ determines an isometry of Teichmuller space with its Weil-Petersson metric whose translation distance ||\psi||_WP is positive. We show there is a constant K >= 1 depending only on the topology of S so that the volume of T_\psi satisfies ||\psi||_WP/K <= vol(T_\psi) <= K ||\psi||_WP.

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