Genericity of pseudo-Anosov mapping classes, when seen as mapping classes

Viveka Erlandsson, Juan Souto, Jing Tao

Research output: Contribution to journalArticle (Academic Journal)peer-review


We prove that pseudo-Anosov mapping classes are generic with respect to certain notions of genericity reflecting that we are dealing with mapping classes. More precisely, we consider a number of functions ρ on the mapping class group, and show that the proportion of pseudo-Anosov mapping classes with ρ-value at most R tends to 1 as R tends to infinity. The functions we consider include measuring the complexity of mapping classes using quasi-conformal distortion or Lipschitz distortion. We present a uniform approach to this problem using geodesic currents.

Original languageEnglish
Pages (from-to)419–439
Number of pages21
JournalL'Enseignement mathematique
Issue number3/4
Publication statusPublished - 6 May 2021


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