On the cohomology of SL$_n(\mathbb{Z})$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909105911758848 |
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| author | Ash, Avner |
| author_facet | Ash, Avner |
| contents | Let St denote the Steinberg module of $SL_n(Q)$ tensored with Q. Let Sh denote the sharbly resolution of St. By Borel-Serre duality, $H^{n(n-1)/2-i}(SL_n(Z),Q)$ is isomorphic to $H_i(SL_n(Z),St)$. The latter is isomorphic to the homology of the $SL_n(Z)$-coinvariants of Sh. We produce nonzero classes in $H_i(SL_n(Z),St)$ for certain small $i$ in terms of sharbly cycles and cosharbly cocycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08840 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the cohomology of SL$_n(\mathbb{Z})$ Ash, Avner Number Theory Let St denote the Steinberg module of $SL_n(Q)$ tensored with Q. Let Sh denote the sharbly resolution of St. By Borel-Serre duality, $H^{n(n-1)/2-i}(SL_n(Z),Q)$ is isomorphic to $H_i(SL_n(Z),St)$. The latter is isomorphic to the homology of the $SL_n(Z)$-coinvariants of Sh. We produce nonzero classes in $H_i(SL_n(Z),St)$ for certain small $i$ in terms of sharbly cycles and cosharbly cocycles. |
| title | On the cohomology of SL$_n(\mathbb{Z})$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.08840 |