论文标题
在球形和Hochschild-pirashvili同源性的楔形上的配置空间
Configuration spaces on a wedge of spheres and Hochschild-Pirashvili homology
论文作者
论文摘要
我们研究了在球体楔形上的构型配置空间的紧凑型合理共同体，配备了对称组的自然作用和自由组的外部自动形态的自然作用（f_g）$（f_g）。这些表示形式在数学的看似无关的部分中显示，从曲线的模量空间的共同体到自由组和Hochschild-Pirashvili的共同函数。 我们表明，这些共同体表示形成形成多项式函数，并使用各种几何模型来计算其许多组成因子。我们进一步针对所有$ n \ leq 10 $颗粒的配置完全计算了组成因子。此分析的应用是对对称组动作的新型超指定下限，重量$ 0 $ $ 0 $ $ 0 $组成的$ h^*_ c（m_ {2，n}）$。
We study the compactly supported rational cohomology of configuration spaces of points on wedges of spheres, equipped with natural actions of the symmetric group and the group $Out(F_g)$ of outer automorphisms of the free group. These representations show up in seemingly unrelated parts of mathematics, from cohomology of moduli spaces of curves to polynomial functors on free groups and Hochschild-Pirashvili cohomology. We show that these cohomology representations form a polynomial functor, and use various geometric models to compute many of its composition factors. We further compute the composition factors completely for all configurations of $n\leq 10$ particles. An application of this analysis is a new super-exponential lower bound on the symmetric group action on the weight $0$ component of $H^*_c(M_{2,n})$.
