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A group theoretic criterion for property FA

Author(s): Marc Culler; Karen Vogtmann
Journal: Proc. Amer. Math. Soc. 124 (1996), 677-683.
MSC (1991): Primary 20E08; Secondary 20F28, 20F36, 05C05
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Abstract: We give group-theoretic conditions on a set of generators of a group $G$ which imply that $G$ admits no non-trivial action on a tree. The criterion applies to several interesting classes of groups, including automorphism groups of most free groups and mapping class groups of most surfaces.

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Additional Information:

Marc Culler
Affiliation: Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607-7045
Email: culler@math.uic.edu

Karen Vogtmann
Affiliation: Department of Mathematics, Cornell University, White Hall, Ithaca, New York 14853-7901
Email: vogtmann@math.cornell.edu

DOI: 10.1090/S0002-9939-96-03217-0
PII: S 0002-9939(96)03217-0
Keywords: Property FA, group actions on trees
Received by editor(s): May 31, 1994
Additional Notes: Both authors are partially supported by the National Science Foundation.
Communicated by: James West
Copyright of article: Copyright 1996, American Mathematical Society

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