论文标题
mod $ p $无序配置空间的同源
Mod $p$ homology of unordered configuration spaces of surfaces
论文作者
论文摘要
我们提供了一个简短的证明，即无序配置空间的mod $ p $同源群的尺寸$ b_k（t）$ k $ suption y torus中的尺寸与$ p> 2 $和$ k \ \ leq p $的betti号码相同。因此，整体同源性没有$ p $ - 功率扭转。同样的论点适用于$ g> 0 $的刺穿属$ g $表面，从而通过卢宾 - 泰特理论恢复了Brantner-Hahn-Knudsen的结果。
We provide a short proof that the dimensions of the mod $p$ homology groups of the unordered configuration space $B_k(T)$ of $k$ points in a torus are the same as its Betti numbers for $p>2$ and $k\leq p$. Hence the integral homology has no $p$-power torsion. The same argument works for the punctured genus $g$ surface with $g>0$, thereby recovering a result of Brantner-Hahn-Knudsen via Lubin-Tate theory.
