2002/10/01 by Louis Funar, Funar, Louis, Christophe Kapoudjian +1 · 1 citation
Mathematics · #20 F 38 #57 N 05 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.GR #math.GT #msc:05 #msc:20 #msc:38 #msc:57
paper · pdf · doi:10.48550/arxiv.math/0210007
G.A.F.A., to appear, 46 p. The paper has been split, this version is the revision of the first part
openalex publication_date 2002/10/01 · arxiv created 2004/09/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to introduce a group containing the mapping class groups of all genus zero surfaces. Roughly speaking, such a group is intended to be a discrete analogue of the diffeomorphism group of the circle. One defines indeed a \it universal mapping class group of genus zero, denoted \B. The latter is a nontrivial extension of the Thompson group V (acting on the Cantor set) by an inductive limit of pure mapping class groups of all genus zero surfaces. We prove that \B is a finitely presented group, and give an explicit presentation of it.