Year: 2026
Type: preprint
Abstract: Brown-Guentner and Haagerup-Przybyszewska showed that every discrete group admits a proper affine isometric action on the universal Banach space $\bigoplus_{p=1}^{\infty} \ell^{2p}(\mathbb{N}),$ taken as the $\ell^{2}$-direct sum, and hence admits a coarse embedding into this space [7, 28]. They further asked whether such embeddings could be used to study the Novikov conjecture. In this paper, we address this question by proving that the strong Novikov conjecture holds for any discrete group that admits a coarse embedding with finite complexity into this universal Banach space. Finally, we show that the recently discovered non-sofic groups constructed by Kun and Thom have Property A and therefore satisfy the Novikov conjecture.
Source: arXiv (Cornell University)
Authors: Tian, Geng, Yu, Guoliang
Institutions: Liaoning University, Texas A&M University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7161137313