Bounded Cohomology and Unitary Representations of Automorphism Groups of Regular Trees

2025/07/14 by Zhao, Cunyuan
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.10141

Abstract

We compute the continuous bounded cohomology of the full automorphism groups of regular trees in all positive degrees, with coefficients arising from any irreducible continuous unitary representations. To the author's knowledge, this seems to be the first instance where the continuous bounded cohomology is determined in all positive degrees with coefficients arising from any irreducible continuous unitary representations without being zero in all cases.

Citations

• Flatmates and the bounded cohomology of algebraic groups
• An algebraic criterion for the vanishing of bounded cohomology
• Lamplighters and the bounded cohomology of Thompson's group
• The bounded cohomology of SL₂ over local fields and S-integers

Related

• Irreducibly represented Lie groups and Nebbia's CCR conjecture on trees
• The bounded cohomology of SL₂ over local fields and S-integers
• Transgression in bounded cohomology and a conjecture of Monod
• Irreducible finite-index representations of automorphism groups of trees
• Norm-controlled cohomology of transformation groups