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

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