Symplectic structures on right-angled Artin groups: between the mapping class group and the symplectic group

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 Gamma is defined to be a subgroup of the automorphism group of the right-angled Artin group A_Gamma of Gamma. We also prove that the kernel of the map Aut A_Gamma to Aut H_1(A_Gamma) is finitely generated, generalizing a theorem of Magnus.

45 pages

References in corpus (3)

• Automorphisms of two-dimensional right-angled Artin groups
• Dimension of the Torelli group for Out(F_n)
• Peak reduction and finite presentations for automorphism groups of right-angled Artin groups

Cited by in corpus (5)

• Peak reduction and finite presentations for automorphism groups of right-angled Artin groups
• Vastness properties of automorphism groups of RAAGs
• Full-featured peak reduction in right-angled Artin groups
• Outer automorphism groups of graph products: subgroups and quotients
• Liftable automorphisms of right-angled Artin groups