Finite abelian subgroups of the mapping class group

Finite abelian subgroups of the mapping class group

Let S be a closed, smooth, orientable surface of genus 2. The mapping class group M of S (or MCG) is the group of isotopy classes of homeomorphisms of S . In this paper we shall investigate the conjugacy classes of finite elementary abelian subgroups, and more generally the finite abelian subgroups of M . While the general finite subgroup classification is important we focus on the case where G...

Abelian and Solvable Subgroups of the Mapping Class Group Joan

1 N ov 2 00 6 Finite abelian subgroups of the mapping class group

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group Mσ of a compact closed surface X of genus σ is considered. A complete method of enumeration is achieved for finite elementary abelian subgroups and steps are taken toward enumera-tion of finite abelian subgroups.

Finite abelian subgroups of the Cremona group of the plane

Finite index subgroups of mapping class groups

Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n...