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arXiv · 2011.03820

Homology of $\GL_n$ over infinite fields outside the stability range

Behrooz Mirzaii
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Abstract

For an infinite field $F$, we study the kernel of the map $H_{n}(\mathrm{GL}_{n-1}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big]) \to H_{n}(\mathrm{GL}_{n}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big])$ and the cokernel of $H_{n+1}\Big(\mathrm{GL}_{n-1}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big]\Big) \to H_{n+1}\Big(\mathrm{GL}_{n}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big]\Big)$. We give conjectural estimates of these kernels and cokernels and prove our conjectures for $n\leq 4$.

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BibTeXRIS

Behrooz Mirzaii. 2020-11-07. Homology of $\GL_n$ over infinite fields outside the stability range. https://doi.org/10.1016/j.jpaa.2021.106916

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