Linearly Bounded Conjugator Property for Mapping Class Groups

2011/06/12 by Jing Tao, Tao, Jing · 3 citations
Computer Science · Mathematics · #2010: 20F34 (Primary) 20F65 #30F60 (Secondary) #57M07 #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1106.2341

openalex publication_date 2011/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• �ber unendliche diskontinuierliche Gruppen

Cited by

• Pseudo-Anosovs from the perspective of their mapping tori
• Residual finiteness properties of some of Halls groups
• Conjugator length of locally compact groups of Euclidean isometries

Related

• Conjugacy classes of big mapping class groups
• Conjugacy Growth and Conjugacy Width of Certain Branch Groups
• Conjugacy languages in groups
• Generating groups by conjugation-invariant sets
• Counting conjugacy classes in groups with contracting elements