Distance in the pants graph and applications to hyperbolic geometry

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• Mehdi Yazdi (KCL)
• Wednesday 06 March 2024, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

The pants graph of a compact orientable surface S, defined by Hatcher and Thurston, is a simplicial graph associated with S. Given two pants decompositions of a compact orientable surface S, we give an upper bound for their distance in the pants graph that depends logarithmically on their intersection number and polynomially on the Euler characteristic of S. As a consequence, we find an upper bound on the volume of the convex core of a maximal cusp (which is a hyperbolic structures on S ×R where given pants decompositions of the conformal boundary are pinched to annular cusps). We also deduce similar upper bounds for distance in the Teichmuller space with the Weil-Petersson metric. This is joint work with Marc Lackenby.

This talk is part of the Differential Geometry and Topology Seminar series.

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