Hopf algebras, Steinberg modules, and the unstable cohomology of $SL_n(\mathbb Z)$ and $GL_n(\mathbb Z)$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911848059633664 |
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| author | Ash, Avner Miller, Jeremy Patzt, Peter |
| author_facet | Ash, Avner Miller, Jeremy Patzt, Peter |
| contents | We prove that the direct sum of all homology groups of the integral general linear groups with Steinberg module coefficients form a commutative Hopf algebra, in particular a free graded commutative algebra. We use this to construct new infinite families of unstable cohomology classes of $SL_n(\mathbb Z)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13776 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hopf algebras, Steinberg modules, and the unstable cohomology of $SL_n(\mathbb Z)$ and $GL_n(\mathbb Z)$ Ash, Avner Miller, Jeremy Patzt, Peter Algebraic Topology K-Theory and Homology Number Theory We prove that the direct sum of all homology groups of the integral general linear groups with Steinberg module coefficients form a commutative Hopf algebra, in particular a free graded commutative algebra. We use this to construct new infinite families of unstable cohomology classes of $SL_n(\mathbb Z)$. |
| title | Hopf algebras, Steinberg modules, and the unstable cohomology of $SL_n(\mathbb Z)$ and $GL_n(\mathbb Z)$ |
| topic | Algebraic Topology K-Theory and Homology Number Theory |
| url | https://arxiv.org/abs/2404.13776 |