Geometry & Topology
- Geom. Topol.
- Volume 13, Number 2 (2009), 857-899.
Symplectic structures on right-angled Artin groups: Between the mapping class group and the symplectic group
We define a family of groups that include the mapping class group of a genus surface with one boundary component and the integral symplectic group . 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 vertices. The mapping class group over the graph is defined to be a subgroup of the automorphism group of the right-angled Artin group of . We also prove that the kernel of is finitely generated, generalizing a theorem of Magnus.
Geom. Topol., Volume 13, Number 2 (2009), 857-899.
Received: 31 July 2008
Accepted: 25 November 2008
First available in Project Euclid: 20 December 2017
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Day, Matthew B. Symplectic structures on right-angled Artin groups: Between the mapping class group and the symplectic group. Geom. Topol. 13 (2009), no. 2, 857--899. doi:10.2140/gt.2009.13.857. https://projecteuclid.org/euclid.gt/1513800219