Homogeneity of the Pure State Space of a Separable $C^*$-Algebra

[摘要] We prove that the pure state space is homogeneous under the action ofthe automorphism group (or the subgroup of asymptotically innerautomorphisms) for all the separable simple $C^*$-algebras. Thefirst result of this kind was shown by Powers for the UHF algbrassome 30 years ago.

[学科分类] 数学（综合）

[关键词] tangle;branched cover;surgery;Heegaard decomposition