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The Bieri-Neumann-Strebel invariant for basis-conjugating automorphisms of free groups

Author: Lisa A. Orlandi-Korner
Journal: Proc. Amer. Math. Soc. 128 (2000), 1257-1262
MSC (2000): Primary 20F28; Secondary 20E08
Published electronically: February 7, 2000
MathSciNet review: 1712889
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Abstract: The pure symmetric automorphism group of the free group on $n$generators, $P\Sigma_n$, consists of those automorphisms which take each generator to a conjugate of itself. We describe the Bieri-Neumann-Strebel invariant of $P\Sigma_n$, which determines, among other things, which subgroups containing the commutator are finitely generated.

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

  • 1. R. Bieri, W. D. Neumann, and R. Strebel, ``A geometric invariant of discrete groups,'' Invent. Math. 90 (1987), 451-477. MR 89b:20108
  • 2. K. S. Brown, ``Trees, valuations, and the Bieri-Neumann-Strebel invariant,'' Invent. Math. 90 (1987), 479-504. MR 89e:20060
  • 3. D. J. Collins, ``Cohomological dimension and symmetric automorphisms of a free group,'' Comment. Math. Helv. 64 (1989), 44-61. MR 90e:20035
  • 4. M. Culler and J. Morgan, ``Group actions on $\mathbf{R}{\text{-tree}}$s,'' Proc. London Math. Soc. 55 (1987), 571-604. MR 88f:20055
  • 5. D. L. Goldsmith, ``The theory of motion groups,'' Mich. Math. J. 28 (1981), 3-17. MR 82h:57007
  • 6. M. Gutiérrez and S. Krstic, ``Normal forms for basis-conjugating automorphisms of a free group,'' preprint.
  • 7. G. Levitt, `` $\mathbf{R}{\text{-tree}}$s and the Bieri-Neumann-Strebel Invariant,'' Publ. Mat. 38 (1994), 195-202. MR 95f:20045
  • 8. J. McCool, ``On basis-conjugating automorphisms of free groups,'' Can. J. Math. 38 (1986), 1525-1529. MR 87m:20093
  • 9. H. Meinert, ``The Bieri-Neumann-Strebel invariants for graph products of groups,'' J. Pure Appl. Alg. 103 (1995), 205-210. MR 96i:20047
  • 10. J. W. Morgan, ``$\Lambda$-trees and their applications,'' Bull. Amer. Math. Soc. 26 (1992), 87-112. MR 92e:20017

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Additional Information

Lisa A. Orlandi-Korner
Affiliation: Department of Mathematics, Cornell University, White Hall, Ithaca, New York 14853
Address at time of publication: Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska 68588-0323

Received by editor(s): March 15, 1998
Published electronically: February 7, 2000
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 2000 American Mathematical Society