Distance in the pants graph and applications to Teichmuller space

Mehdi Yazdi (King's College London)

Monday 11th November 16:00-17:00 Maths 311B

Abstract

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 structure on S x R where given pants decompositions of the conformal boundary are pinched to annular cusps). As a further application, we give an upper bound for the Weil–Petersson distance between two points in the Teichmuller space of S in terms of their corresponding short pants decompositions. This is joint work with Marc Lackenby. 

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