Higher Kazhdan projections and delocalized $\ell^2$-Betti numbers for an amalgamated product group
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913932237602816 |
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| author | Ren, Baiying |
| author_facet | Ren, Baiying |
| contents | We establish explicit expressions for the $K$-theory classes of higher Kazhdan projections for amalgamated product groups $\mathbb{Z}_m*_{\mathbb{Z}_d}\mathbb{Z}_n$. Our approach follows the methodology developed by Pooya and Wang for free product groups $\mathbb{Z}_m*\mathbb{Z}_n$, and naturally generalizes their results on free products. As an application of the $K$-class expressions, we obtain non-vanishing results for delocalized $\ell^2$-Betti numbers of $\mathrm{SL}(2,\mathbb{Z})$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_05787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Kazhdan projections and delocalized $\ell^2$-Betti numbers for an amalgamated product group Ren, Baiying Operator Algebras Group Theory K-Theory and Homology 46L80, 20F65, 20J05, 20E06 We establish explicit expressions for the $K$-theory classes of higher Kazhdan projections for amalgamated product groups $\mathbb{Z}_m*_{\mathbb{Z}_d}\mathbb{Z}_n$. Our approach follows the methodology developed by Pooya and Wang for free product groups $\mathbb{Z}_m*\mathbb{Z}_n$, and naturally generalizes their results on free products. As an application of the $K$-class expressions, we obtain non-vanishing results for delocalized $\ell^2$-Betti numbers of $\mathrm{SL}(2,\mathbb{Z})$. |
| title | Higher Kazhdan projections and delocalized $\ell^2$-Betti numbers for an amalgamated product group |
| topic | Operator Algebras Group Theory K-Theory and Homology 46L80, 20F65, 20J05, 20E06 |
| url | https://arxiv.org/abs/2507.05787 |