Norm growth for the Busemann cocycle

zbMATH Open1504.20031arXiv1704.02274MaRDI QIDQ668620

Thibaut Dumont

Publication date: 19 March 2019

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Abstract: Using explicit methods, we provide an upper bound to the norm of the Busemann cocycle of a locally finite regular tree $X$, emphasizing the symmetries of the cocycle. The latter takes value into a submodule of square summable functions on the edges of $X$, which corresponds the Steinberg representation for rank one groups acting on their Bruhat-Tits tree. The norm of the Busemann cocycle is asymptotically linear with respect to square root of the distance between any two vertices. Independently, Gournay and Jolissaint proved an exact formula for harmonic 1-cocycles covering the present case.

Full work available at URL: https://arxiv.org/abs/1704.02274

zbMATH Keywords

Steinberg representationcocycle growthgroup acting on trees

Mathematics Subject Classification ID

Geometric group theory (20F65) Cohomology of groups (20J06) Groups acting on trees (20E08)

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