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PreprintCC BY-NC-SA 4.0arXiv

Higher Kazhdan projections for one relator groups

  • Sanaz Pooya
  • Baiying Ren
  • Hang Wang
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Abstract

We study the K-theory classes of higher Kazhdan projections of a discrete group under a spectral-gap assumption and recall how they are obtained, via the Baum--Connes assembly map, from equivariant Euler classes. After reviewing the case of virtually free groups, where the universal space for proper actions has a one-dimensional model, we prove the main new result: an explicit description of the K-theory class of the first higher Kazhdan projection for finitely generated infinite one-relator groups whose first Laplacian has a spectral gap. If moreover the one-relator group is hyperbolic, this also gives corresponding formulas for delocalised ℓ2-Betti numbers.

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Cite

BibTeXRIS
BibTeX
@misc{pooya2026higher,
  title = {{Higher Kazhdan projections for one relator groups}},
  author = {Sanaz Pooya and Baiying Ren and Hang Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00493},
  eprint = {2609.00493},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00493},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Higher Kazhdan projections for one relator groups
AU  - Sanaz Pooya
AU  - Baiying Ren
AU  - Hang Wang
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00493
UR  - https://arxiv.org/abs/2609.00493
AB  - We study the K-theory classes of higher Kazhdan projections of a discrete group under a spectral-gap assumption and recall how they are obtained, via the Baum--Connes assembly map, from equivariant Euler classes. After reviewing the case of virtually free groups, where the universal space for proper actions has a one-dimensional model, we prove the main new result: an explicit description of the K-theory class of the first higher Kazhdan projection for finitely generated infinite one-relator groups whose first Laplacian has a spectral gap. If moreover the one-relator group is hyperbolic, this also gives corresponding formulas for delocalised ℓ^2-Betti numbers.
ER  -