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PreprintCC BY 4.0arXiv

Embedding complexity into the universal Banach space and the strong Novikov conjecture

  • Geng Tian
  • Guoliang Yu
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Abstract

Brown-Guentner and Haagerup-Przybyszewska showed that every discrete group admits a proper affine isometric action on the universal Banach space ⨁p=1∞ ℓ2p(ℕ), taken as the ℓ2-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.

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Cite

BibTeXRIS
BibTeX
@misc{tian2026embedding,
  title = {{Embedding complexity into the universal Banach space and the strong Novikov conjecture}},
  author = {Geng Tian and Guoliang Yu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.12930},
  eprint = {2605.12930},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.12930},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Embedding complexity into the universal Banach space and the strong Novikov conjecture
AU  - Geng Tian
AU  - Guoliang Yu
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2605.12930
UR  - https://arxiv.org/abs/2605.12930
AB  - Brown-Guentner and Haagerup-Przybyszewska showed that every discrete group admits a proper affine isometric action on the universal Banach space ⨁_p=1^∞ ℓ^2p(ℕ), taken as the ℓ^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.
ER  -