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arXiv · 2510.12058

On proper affine actions with better decaying cocycles

Chunliu Feng·Geng Tian·Ran Yi
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Abstract

It is well-known that the study of proper affine isometric actions of countable discrete groups in various spaces plays a crucial role in geometric group theory, operator algebras, and high-dimensional topology. In this article, we shall construct a proper affine isometric action of countable discrete group $\Gamma$ on the Banach space $\oplus_{n=1}^\infty\ell^{2n}(\Gamma)$ such that the cocycles have decay rates that are better than those of Haagerup and Przybyszewska in.

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Chunliu Feng, Geng Tian, Ran Yi. 2025-10-14. On proper affine actions with better decaying cocycles. https://arxiv.org/abs/2510.12058

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