Communications in Analysis and Geometry

Volume 11 (2003)

Number 5

Weil-Petersson Translation Distance and Volumes of Mapping Tori

Pages: 987 – 999

DOI: http://dx.doi.org/10.4310/CAG.2003.v11.n5.a6

Author

Jeffrey F. Brock

Abstract

Given a closed hyperbolic 3-manifold Tψ that fibers over the circle with monodromy ψ: S → S , the monodromy ψ determines an isometry of Teichmüller space with itsWeil-Petersson metric whose translation distance ∥ψ∥WP is positive. We show there is a constant K ≥ 1 depending only on the topology of S so that the volume of Tψ satisfies

∥ψ∥WP/K ≤ vol(Tψ) ≤ K∥ψ∥ WP.

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