Illinois Journal of Mathematics

The Bieri–Neumann–Strebel invariant of the pure symmetric automorphisms of a right-angled Artin group

Nic Koban and Adam Piggott

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Abstract

We compute the BNS-invariant for the pure symmetric automorphism groups of right-angled Artin groups. We use this calculation to show that the pure symmetric automorphism group of a right-angled Artin group is itself not a right-angled Artin group provided that its defining graph contains a separating intersection of links.

Article information

Source
Illinois J. Math., Volume 58, Number 1 (2014), 27-41.

Dates
First available in Project Euclid: 1 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1427897167

Digital Object Identifier
doi:10.1215/ijm/1427897167

Mathematical Reviews number (MathSciNet)
MR3331840

Zentralblatt MATH identifier
1332.20044

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Citation

Koban, Nic; Piggott, Adam. The Bieri–Neumann–Strebel invariant of the pure symmetric automorphisms of a right-angled Artin group. Illinois J. Math. 58 (2014), no. 1, 27--41. doi:10.1215/ijm/1427897167. https://projecteuclid.org/euclid.ijm/1427897167


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References

  • R. Bieri, W. D. Neumann and R. Strebel, A geometric invariant of discrete groups, Invent. Math. 90 (1987), no. 3, 451–477.
  • K. S. Brown, Trees, valuations, and the Bieri–Neumann–Strebel invariant, Invent. Math. 90 (1987), no. 3, 479–504.
  • R. Charney, K. Ruane, N. Stambaugh and A. Vijayan, The automorphism group of a graph product with no SIL, Illinois J. Math. 54 (2010), no. 1, 249–262.
  • M. Gutierrez, A. Piggott and K. Ruane, On the automorphisms of a graph product of Abelian groups, Groups Geom. Dyn. 6 (2012), no. 1, 125–153.
  • M. R. Laurence, A generating set for the automorphism group of a graph group, J. Lond. Math. Soc. (2) 52 (1995), no. 2, 318–334.
  • J. Meier and L. VanWyk, The Bieri–Neumann–Strebel invariants for graph groups, Proc. Lond. Math. Soc. (3) 3 (1995), no. 2, 263–280.
  • L. Orlandi-Korner, The Bieri–Neumann–Strebel invariant for basis-conjugating automorphisms of free groups, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1257–1262.
  • E. Toinet, Automorphismes des groupes d'Artin à angles droits, Ph.D. thesis, Université de Bourgogne, 2012.