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Fixed points of finite groups of free group automorphisms


Author: Tad White
Journal: Proc. Amer. Math. Soc. 118 (1993), 681-688
MSC: Primary 57M07; Secondary 20E08
DOI: https://doi.org/10.1090/S0002-9939-1993-1164152-7
MathSciNet review: 1164152
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Abstract: We construct an equivariant collection of contractions of the compactified Culler-Vogtmann outer space $ {\overline X _n}$. As a consequence, we prove that any finite subgroup of the outer automorphism group of a free group fixes a contractible subset of $ {\bar X_n}$.


References [Enhancements On Off] (What's this?)

  • [Cu] M. Culler, Finite groups of automorphisms of a free group, Contributions to Group Theory, Contemp. Math., vol. 33, Amer. Math. Soc., Providence, RI, 1984, pp. 197-207. MR 767107 (86g:20027)
  • [CM] M. Culler and J. W. Morgan, Group actions on $ {\mathbf{R}}$-trees, Proc. London Math. Soc. (3) 55 (1987), 571-604. MR 907233 (88f:20055)
  • [CV] M. Culler and K. Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986), 91-119. MR 830040 (87f:20048)
  • [G] M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes. Études Sci. Publ. Math. 53 (1981), 53-78. MR 623534 (83b:53041)
  • [KV] S. Krstić and K. Vogtmann, Equivariant outer space and automorphisms of free-by-finite groups, preprint. MR 1214230 (94c:20067)
  • [P] F. Paulin, The Gromov topology on $ {\mathbf{R}}$-trees, Topology Appl. 32 (1989), 197-221. MR 1007101 (90k:57015)
  • [Sk] R. Skora, Deformations of length functions in groups, preprint.
  • [St] M. Steiner, Ph.D. thesis, Columbia University, 1988.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1164152-7
Keywords: Length function, tree, outer space
Article copyright: © Copyright 1993 American Mathematical Society

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