Constructing convex planes in the pants complex

DOI10.1090/S0002-9939-09-09907-9zbMath1177.57010arXivmath/0702837OpenAlexW2013063317MaRDI QIDQ3182590

Hugo Parlier, Javier Aramayona, Kenneth J. Shackleton

Publication date: 9 October 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702837

zbMATH Keywords

Weil-Petersson metricpants complex

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Distance in graphs (05C12)

Related Items (5)

Hyperbolicity of the genus two Hatcher-Thurston complex. ⋮ Geodesic axes in the pants complex of the five-holed sphere ⋮ Products of Farey graphs are totally geodesic in the pants graph ⋮ Geometric simplicial embeddings of arc-type graphs ⋮ The geometry of flip graphs and mapping class groups

Cites Work

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• Totally geodesic subgraphs of the pants complex
• Coarse and synthetic Weil-Petersson geometry: Quasi-flats, geodesics and relative hyperbolicity
• Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity.
• A presentation for the mapping class group of a closed orientable surface
• Noncompleteness of the Weil-Petersson metric for Teichmüller space
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• Automorphisms of the pants complex
• Geometry of the complex of curves. II: Hierarchical structure
• Geodesic length functions and the Nielsen problem
• Curvature and rank of Teichmuller space
• The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores

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