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Groups acting faithfully on trees and properly on products of trees

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arxiv 1910.04614 v1 pith:LLEQHBPZ submitted 2019-10-10 math.GR

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classification math.GR
keywords treesfinitegroupsproductproperlyactionevidencelocally
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We examine the question of which finitely generated groups act properly on a finite product of simplicial trees, considering both arbitrary trees and where all trees are locally finite. In the second case we present evidence in favour of hyperbolic surface groups having such an action. However we also present evidence that many RAAGs do not admit such an action and we give an example of a virtually special group which does not act properly preserving factors on any finite product of locally finite trees, even though it does so on a product of three trees without the local finiteness condition.

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  1. Bounded cohomology of groups acting on trees with almost prescribed local actions

    math.GR 2024-12 conditional novelty 7.0 of 10

    For the groups G(F,F'), if F' is 2-transitive then the group is boundedly acyclic; otherwise its second bounded cohomology is infinite dimensional.

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