分枝覆盖的量子化
Quantization of branched coverings
摘要：
我们用C（X）上的Hilbert C*-模C（Y）和具有指数-有限型拓扑的忠实单位正条件期望E：C（Y）->C（X）来确定分支覆盖（T2空间的连续开满射p：Y->X，其原像数一致有界）.非分支覆盖的情况对应于投射有限生成模和指数有限型的期望（代数上）。这允许定义（分支）覆盖的非交换类似物。
英文摘要：
We identify branched coverings (continuous open surjections p:Y->X of Hausdorff spaces with uniformly bounded number of pre-images) with Hilbert C*-modules C(Y) over C(X) and with faithful unital positive conditional expectations E:C(Y)->C(X) topologically of index-finite type. The case of non-branched coverings corresponds to projective finitely generated modules and expectations (algebraically) of index-finite type. This allows to define non-commutative analogues of (branched) coverings.
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