论文标题
关于自由群体的IA-Automormormoright群体的稳定共同体学
On the stable cohomology of the IA-automorphism groups of free groups
论文作者
论文摘要
Borel的稳定性和消失定理给出了$ \ Mathrm {gl}（n，\ Mathbb {Z}）$的稳定共同体，并在代数$ \ Mathrm {gl}（n，n，\ mathbb {z}）中具有系数。通过将Borel定理与Hochschild-Serre频谱序列相结合，我们计算了自由态度组$ \ MATHRM {aut}（f_n）$ f_n $ f_n $ cANK $ n $的扭曲的第一组共同体。我们还研究了$ f_n $的IA-Automormormorming群体$ \ MATHRM {ia} _n $的稳定理性共同体。我们提出了$ \ mathrm {ia} _n $的稳定有理共同体的猜想代数结构，并考虑了与已知结果和猜想的某些关系。我们还考虑了Torelli表面组稳定的理性共同体的猜想结构。
Borel's stability and vanishing theorem gives the stable cohomology of $\mathrm{GL}(n,\mathbb{Z})$ with coefficients in algebraic $\mathrm{GL}(n,\mathbb{Z})$-representations. By combining the Borel theorem with the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group $\mathrm{Aut}(F_n)$ of the free group $F_n$ of rank $n$. We also study the stable rational cohomology of the IA-automorphism group $\mathrm{IA}_n$ of $F_n$. We propose a conjectural algebraic structure of the stable rational cohomology of $\mathrm{IA}_n$, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces.
