On Chern classes of almost representations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915520164397056 |
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| author | Dadarlat, Marius Glebe, Forrest |
| author_facet | Dadarlat, Marius Glebe, Forrest |
| contents | For a discrete group $Γ$, we study vector bundles $E_ρ$ on compact subsets of $BΓ$ associated to almost representations $ρ:Γ\to U(n)$. We compute the first Chern class of $E_ρ$ in terms of $ρ$. When $ρ$ is both projective and almost multiplicative, we determine its Chern character. These invariants yield obstructions to perturbing almost representations to those arising from projective representations. For residually finite amenable groups, the $K$-theory classes of $E_ρ$ classify almost representations up to stable equivalence. Finally, for $\mathbb{Z}^d$, $\mathbb{Z}\times \mathbb{H}_3$, and $\mathbb{H}_3\times \mathbb{H}_3$, we construct explicit almost representations with prescribed Chern classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23950 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Chern classes of almost representations Dadarlat, Marius Glebe, Forrest K-Theory and Homology Group Theory Operator Algebras For a discrete group $Γ$, we study vector bundles $E_ρ$ on compact subsets of $BΓ$ associated to almost representations $ρ:Γ\to U(n)$. We compute the first Chern class of $E_ρ$ in terms of $ρ$. When $ρ$ is both projective and almost multiplicative, we determine its Chern character. These invariants yield obstructions to perturbing almost representations to those arising from projective representations. For residually finite amenable groups, the $K$-theory classes of $E_ρ$ classify almost representations up to stable equivalence. Finally, for $\mathbb{Z}^d$, $\mathbb{Z}\times \mathbb{H}_3$, and $\mathbb{H}_3\times \mathbb{H}_3$, we construct explicit almost representations with prescribed Chern classes. |
| title | On Chern classes of almost representations |
| topic | K-Theory and Homology Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2509.23950 |