论文标题
通勤元素的配置空间
Configuration spaces of commuting elements
论文作者
论文摘要
在本文中，我们介绍了拓扑组中通勤元素的配置空间，并表明它满足了单一，特殊统一和符号群的序列的合理同源稳定性。我们还证明，它满足了此类群体有限产物的元组元素的数量，特别是在通勤元素的无序配置的空间中，它满足了元组中的元素数量。最后，我们在不稳定范围内介绍了一些共同体学计算。
In this article we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary and symplectic groups. We also prove that it satisfies cohomological rational representation stability with respect to the number of elements in the tuple for finite products of such groups, in particular cohomological rational stability for the space of unordered configurations of commuting elements. Finally we present some computations of cohomology in the unstable range.
