\(\mathbb{R}\)-trees and the Bieri-Neumann-Strebel invariant. (English) Zbl 0829.20038

Levitt, Gilbert

Publ. Mat., Barc. 38, No. 1, 195-202 (1994).

For a finitely generated group \(G\) a new characterization of the invariant \(\Sigma(G)\) [see R. Bieri, W. D. Neumann and R. Strebel, Invent. Math. 90, 451-477 (1987; Zbl 0642.57002)] in terms of special actions of \(G\) on \(\mathbb{R}\)-trees is given. K. S. Brown’s characterization of \(\Sigma\) [ibid., 479-504 (1987; Zbl 0663.20033)] is reproved in the same manner.

Reviewer: Yu.N.Mukhin (Ekaterinburg)

MSC:

20E08	Groups acting on trees
57M05	Fundamental group, presentations, free differential calculus
20F65	Geometric group theory

Keywords:

actions on \(\mathbb{R}\)-trees; finitely generated groups

Citations:

Zbl 0642.57002; Zbl 0663.20033