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DYNAMICS ON THE PERFECT KERNEL OF NON-AMENABLE HIGHER-RANK GENERALIZED BAUMSLAG-SOLITAR GROUPS
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- Journal:
- Journal of the Institute of Mathematics of Jussieu , First View
- Published online by Cambridge University Press:
- 15 October 2026, pp. 1-39
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In this article, we study the space of subgroups of non-amenable generalized Baumslag-Solitar groups (GBS groups) of rank d, that is, groups acting cocompactly on an oriented tree with vertex and edge stabilizers isomorphic to $\mathbb {Z}^d$
. Our results generalize the study of Baumslag-Solitar groups, and of GBS groups of rank $1$
. We give an explicit description of the perfect kernel of a non-amenable GBS group G of rank d and show the existence of a partition of the perfect kernel into a countably infinite set of pieces that are invariant under the action by conjugation of G, and such that each piece contains a dense orbit.
Browder's Convergence for One-Parameter Nonexpansive Semigroups
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- Journal:
- Canadian Mathematical Bulletin / Volume 55 / Issue 1 / 01 March 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 15-25
- Print publication:
- 01 March 2012
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