Weil-Petersson translation distance and volumes of mapping tori
نویسنده
چکیده
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 its Weil-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.
منابع مشابه
Entropy, Weil-petersson Translation Distance and Gromov Norm for Surface Automorphisms
Thanks to a theorem of Brock on the comparison of Weil-Petersson translation distances and hyperbolic volumes of mapping tori for pseudoAnosovs, we prove that the entropy of a surface automorphism in general has linear bounds in terms of a Gromov norm of its mapping torus from below and an inbounded geometry case from above. We also prove that the WeilPetersson translation distance does the sam...
متن کاملEntropy versus Volume for Pseudo-Anosovs
We discuss a comparison of the entropy of pseudo-Anosov maps and the volume of their mapping tori. Recent study of Weil-Petersson geometry of the Teichmüller space tells us that they admit linear inequalities for both directions under some bounded geometry condition. Based on the experiments, we present various observations on the relation between minimal entropies and volumes, and on bounding ...
متن کاملThe Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores
We introduce a coarse combinatorial description of the Weil-Petersson distance dWP(X, Y ) between two finite area hyperbolic Riemann surfaces X and Y . The combinatorics reveal a connection between Riemann surfaces and hyperbolic 3-manifolds conjectured by Thurston: the volume of the convex core of the quasi-Fuchsian manifold Q(X, Y ) with X and Y in its boundary is comparable to the Weil-Peter...
متن کاملModuli spaces of hyperbolic surfaces and their Weil–Petersson volumes
Moduli spaces of hyperbolic surfaces may be endowed with a symplectic structure via the Weil–Petersson form. Mirzakhani proved that Weil–Petersson volumes exhibit polynomial behaviour and that their coefficients store intersection numbers on moduli spaces of curves. In this survey article, we discuss these results as well as some consequences and applications.
متن کاملEstimates of Weil-petersson Volumes via Effective Divisors
The Mumford class κ1 on Mg,0 was shown to be proportional to the cohomology class [ωWP ] of the Weil-Petersson form by Wolpert in [WO]. Furthermore he showed that the restriction of this class to any component of the compactyfying divisor coincides with the corresponding Weil-Petersson class. Arbarello and Cornalba introduced classes κ1 on Mg,n, proved a similar restriction property for these a...
متن کامل