非阿贝尔GKM理论
Non-abelian GKM Theory
摘要：
本文将GKM理论推广到任意紧连通李群的作用。对于满足非阿贝尔GKM条件的动作，我们附加一个编码非阿贝尔1-骨架结构的图，即，点的子空间，其合痕秩至多比作用群的秩小小于一。我们证明了等变上同调的代数结构可以从这个图中读出。与一般的阿贝尔GKM理论相比，由于非阿贝尔1-骨架的结构更为复杂，因而具有一些特殊的性质。
英文摘要：
We describe a generalization of GKM theory for actions of arbitrary compact connected Lie groups. To an action satisfying the non-abelian GKM conditions we attach a graph encoding the structure of the non-abelian 1-skeleton, i.e., the subspace of points with isotopy rank at most one less than the rank of the acting group. We show that the algebra structure of the equivariant cohomology can be read off from this graph. In comparison with ordinary abelian GKM theory, there are some special features due to the more complicated structure of the non-abelian 1-skeleton.
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