Linearly Bounded Conjugator Property for Mapping Class Groups
arXiv:1106.2341
Abstract
Given two conjugate mapping classes f and g, we produce a conjugating element w such that |w| < K(|f|+|g|), where |.| denotes the word metric with respect to a fixed generating set, and K is a constant depending only on the generating set. As a consequence, the conjugacy problem for mapping class groups is exponentially bounded.
43 pages, 3 figures. Referee's comments incorporated. To appear in GAFA