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Automorphisms of
$2$–dimensional right-angled Artin groups
Ruth Charney, John Crisp and Karen Vogtmann |
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Geometry & Topology 11 (2007) 2227–2264
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arXiv: math/0610980v2 |
Abstract |
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We study the outer automorphism group of a right-angled Artin group in the case where the defining graph is connected and triangle-free. We give an algebraic description of in terms of maximal join subgraphs in and prove that the Tits’ alternative holds for . We construct an analogue of outer space for and prove that it is finite dimensional, contractible, and has a proper action of . We show that has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most general upper bound. |
Keywords
right-angled Artin groups, outer automorphisms, outer space
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Mathematical Subject Classification 2000
Primary: 20F36
Secondary: 20F65, 20F28
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References |
Forward citations |
Publication
Received: 4 August 2007
Accepted: 7 September 2007
Published: 14 November 2007
Proposed: John Morgan
Seconded: Martin Bridson, Joan Birman
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Authors |
| Ruth Charney | |
| Department of Mathematics Brandeis University Waltham MA 02454-9110 USA |
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| http://people.brandeis.edu/~charney/ | |
| John Crisp | |
| Institut de Mathematiques de
Bourgogne Université de Bourgogne B P 47 870 21078 Dijon Cedex France |
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| Karen Vogtmann | |
| Department of Mathematics Cornell University Ithaca NY 14853-4201 USA |
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| http://www.math.cornell.edu/~vogtmann/ | |
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