Abstract
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 language | English |
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Pages (from-to) | 419–439 |
Number of pages | 21 |
Journal | L'Enseignement mathematique |
Volume | 66 |
Issue number | 3/4 |
DOIs | |
Publication status | Published - 6 May 2021 |