Volume 13, issue 2 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Symplectic structures on right-angled Artin groups: Between the mapping class group and the symplectic group

Matthew B Day

Geometry & Topology 13 (2009) 857–899
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, ). 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 AΓ of Γ. We also prove that the kernel of AutAΓ AutH1(AΓ) is finitely generated, generalizing a theorem of Magnus.

Keywords
peak reduction, symplectic structure, finite generation, right-angled Artin group
Mathematical Subject Classification 2000
Primary: 20F36, 20F28
References
Publication
Received: 31 July 2008
Accepted: 25 November 2008
Published: 8 January 2009
Proposed: Joan Birman
Seconded: Leonid Polterovich, Ron Stern
Authors
Matthew B Day
Department of Mathematics
California Institute of Technology
1200 E California Blvd
Pasadena, CA 91101
USA
http://www.its.caltech.edu/~mattday