On a universal mapping class group of genus zero

Abstract

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.

G.A.F.A., to appear, 46 p. The paper has been split, this version is the revision of the first part

References in corpus (1)

• An extension of the Burau representation to a mapping class group associated to Thompson's group T