发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对纯$C^*$-代数，证明了与任意正元同Cuntz类的正元集合道路连通，推广了投影类同伦理论，扩展了相关拓扑结果的适用范围。
AI 中文摘要
设$A$是一个单位元、单、可分且纯的$C^*$-代数。我们证明，对每个$a\in A_+$（$A$中的正元），与$a$具有相同Cuntz类的正元集合是道路连通的。这可视为投影类经典同伦理论向正元的推广，将此前需更强正则性假设的常Cuntz类拓扑系列结果扩展到纯$C^*$-代数类，该类特别包含所有无自同构代数。
英文摘要
Let $A$ be a unital, simple, separable, and pure $C^*$-algebra. We prove that, for every $a\in A_+$, the set of positive elements in $A$ having the same Cuntz class as $a$ is path-connected. This may be viewed as a generalization to positive elements of the classical homotopy theory of projection classes and extends a line of results on the topology of constant Cuntz classes that previously required stronger regularity hypotheses to the class of pure $C^*$-algebras, which notably contains all selfless algebras.
Comments9 pages, no figures
