Centroids and the Rapid Decay property in mapping class groups

Abstract

We study a notion of a Lipschitz, permutation-invariant "centroid" for triples of points in mapping class groups MCG(S), which satisfies a certain polynomial growth bound. A consequence (via work of Drutu-Sapir or Chatterji-Ruane) is the Rapid Decay Property for MCG(S).

arXiv commentv3. Numerous typos fixed and some arguments elucidated

Cited by in corpus (4)

• Hierarchically hyperbolic spaces II: Combination theorems and the distance formula
• Stable cubulations, bicombings, and barycenters
• Coarse median structures and homomorphisms from Kazhdan groups
• Higher rank lattices are not coarse median