Geometry & Topology 13 (2009) 857–899

DOI: 10.2140/gt.2009.13.857

Abstract

We define a family of groups that include the mapping class group of a genus g surface with one boundary component and the integral symplectic group Sp(2g, Z). We then prove that these groups are finitely generated. These groups, which we call mapping class groups over graphs, are indexed over labeled simplicial graphs with 2g vertices. The mapping class group over the graph Γ is defined to be a subgroup of the automorphism group of the right-angled Artin group A_Γ of Γ. We also prove that the kernel of AutA_Γ → AutH₁(A_Γ) is finitely generated, generalizing a theorem of Magnus.

Keywords

peak reduction, symplectic structure, finite generation, right-angled Artin group

Mathematical Subject Classification

Primary: 20F28, 20F36

References

Publication

Received: 31 July 2008
Accepted: 25 November 2008
Published: 8 January 2009
Proposed: Joan Birman
Seconded: Leonid Polterovich, Ron Stern

Authors