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

Abstract

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

26 pages, Latex

References in corpus (1)

• Homological stability for classical groups