Symplectic structures on right-angled Artin groups: Between the mapping class group and the symplectic group
نویسندگان
چکیده
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 is defined to be a subgroup of the automorphism group of the right-angled Artin group A of . We also prove that the kernel of AutA!AutH1.A/ is finitely generated, generalizing a theorem of Magnus.
منابع مشابه
RAAGs in Ham
We prove that every RAAG (Right Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of every symplectic manifold.
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