Weil-Petersson Translation Distance and Volumes of Mapping Tori

By Jeffrey F. Brock. 2001

62 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ae423b3b6dc2b4b773f6a01e7852f8d3b38f89fa

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Dynamical degrees of birational transformations of projective surfaces (2013, methodology): “The volume of Mφ with respect to this riemannian metric is a positive real number vol(φ); this volume is, up to a bounded multiplicative error, the translation length of φ on the Teichmüller space with respect to the Weil-Petersson metric (see [13]).”
Problems on invariants of knots and 3-manifolds (2004, background): “Brock [68] that the volume of a mapping torus is quasi-linear in the pants translation distance (for fixed genus).”
Tameness of hyperbolic 3-manifolds (2004, methodology): “The following arguments are modifications of work of Brock in [14], as a way of generalizing the simplicial ruled surface interpolation techniques of Thurston [55] and Canary [19].”
On Canonical Triangulations of Once-Punctured Torus Bundles and Two-bridge link complements (2004, background): “Geometry & Topology 10 (2006) 1239–1284 1239 arXiv version: fonts, pagination and layout may vary from GT published version”