Geometry of the Weil-Petersson completion of Teichm\

By S. Wolpert. 2005

161 citations recorded by the source corpus.

We present a view of the current understanding of the geometry of Weil-Petersson (WP) geodesics on the completion of the Teichm\"uller space. We sketch a collection of results by other authors and then proceed to develop the properties of the WP CAT(0) geometry. Our approach includes a simplified proof of the Masur-Wolf theorem, a classification of flats and of geodesic limits.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/935f5c886d1560a1249b860109027a9af8da1959

How researchers see this paper

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In Geometry and Topology

1. A. Zorich
2. H. Masur
3. A. Eskin
4. M. Kontsevich
5. M. Bestvina
6. K. Fujiwara
7. G. Forni
8. Dawei Chen

Citations in the corpus

• Coarse and synthetic Weil–Petersson geometry: quasi-flats, geodesics and relative hyperbolicity (2007, background): “sults of Masur-Minsky [MM2], Brock [Br1], Brock-Farb [BF], Behrstock-Minsky [BM], Rafi [Raf], Wolpert [ Wol2 ], and others giving insight into coarse phenomena that arise in consideration of various metrics.”
• A Characterization of Higher Rank Symmetric Spaces Via Bounded Cohomology (2007, background): “A pseudo-Anosov element, g, in the mapping class group MCG(S) has an invariant geodesic, l, in WP called the axis (see [16]).”
• An analytic construction of the Deligne-Mumford compactification of the moduli space of curves (2013, background): “Wolpert [46], [47], [48], [49], [50], [51], [52], [53], [54].”
• Classification of Weil-Petersson isometries (2002, unknown): “Given c and c′ in C(Σg,n), let i(c, c′) denote the geometric intersection number between them, and for c ∈ C(Σg,n) and After this paper was submitted for publication, we received the preprint [W6] which provides an alternative discussion of these results.”
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow (2011, background): “We also assume that K is sufficiently large so that the core curves of all the cylinders in CylK(S) are short in the hyperbolic metric, see [W2] or [W3].”