Euler characteristics, higher Kazhdan projections and delocalised $\ell^2$-Betti numbers
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912504282611712 |
|---|---|
| author | Pooya, Sanaz Ren, Baiying Wang, Hang |
| author_facet | Pooya, Sanaz Ren, Baiying Wang, Hang |
| contents | For non-amenable finitely generated virtually free groups, we show that the combinatorial Euler characteristic introduced by Emerson and Meyer is the preimage of the K-theory class of higher Kazhdan projections under the Baum-Connes assembly map. This allows to represent the K-theory class of their higher Kazhdan projection as a finite alternating sum of the K-theory classes of certain averaging projections. The latter is associated to the finite subgroups appearing in the fundamental domain of their Bass-Serre tree. As an immediate application we obtain non-vanishing calculations for delocalised $\ell^2$-Betti numbers for this class of groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euler characteristics, higher Kazhdan projections and delocalised $\ell^2$-Betti numbers Pooya, Sanaz Ren, Baiying Wang, Hang Operator Algebras Differential Geometry K-Theory and Homology 46L80, 19D55, 20F65 For non-amenable finitely generated virtually free groups, we show that the combinatorial Euler characteristic introduced by Emerson and Meyer is the preimage of the K-theory class of higher Kazhdan projections under the Baum-Connes assembly map. This allows to represent the K-theory class of their higher Kazhdan projection as a finite alternating sum of the K-theory classes of certain averaging projections. The latter is associated to the finite subgroups appearing in the fundamental domain of their Bass-Serre tree. As an immediate application we obtain non-vanishing calculations for delocalised $\ell^2$-Betti numbers for this class of groups. |
| title | Euler characteristics, higher Kazhdan projections and delocalised $\ell^2$-Betti numbers |
| topic | Operator Algebras Differential Geometry K-Theory and Homology 46L80, 19D55, 20F65 |
| url | https://arxiv.org/abs/2507.20119 |