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Displacement techniques in bounded cohomology

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arxiv 2401.08857 v2 pith:75KMKLD6 submitted 2024-01-16 math.GR math.GT

Caterina Campagnolo , Francesco Fournier-Facio , Yash Lodha , Marco Moraschini This is my paper · ORCID
classification math.GRmath.GT
keywords displacementboundedcohomologytechniquesvanishingalgebraicalongapplicable
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Several algebraic criteria, reflecting displacement properties of transformation groups, have been used in the past years to prove vanishing of bounded cohomology and stable commutator length. Recently, the authors introduced the property of commuting cyclic conjugates, a new displacement technique that is widely applicable and provides vanishing of the bounded cohomology in all positive degrees and all dual separable coefficients. In this note we consider the most recent along with the by now classical displacement techniques and we study implications among them as well as counterexamples.

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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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