论文标题
循环空间的索引定理
An Index Theorem for Loop Spaces
论文作者
论文摘要
我们在$ kk $ -theory的框架中制定并证明了一个紧凑型歧管的循环空间的索引定理。它是Witten属的非交通性几何定义（或分析对应物）的有力候选者。为了找出索引定理的“适当形式”以制定循环空间版本，我们为配备$ S^1 $ actions的非紧凑型歧管制定并证明了具有紧凑型固定点集的非紧密歧管定理。为了制定它，我们使用正式的电源系列。
We formulate and prove an index theorem for loop spaces of compact manifolds in the framework of $KK$-theory. It is a strong candidate for the noncommutative geometrical definition (or the analytic counterpart) of the Witten genus. In order to find out an "appropriate form" of the index theorem to formulate a loop space version, we formulate and prove an equivariant index theorem for non-compact manifolds equipped with $S^1$-actions with compact fixed-point sets. In order to formulate it, we use a ring of formal power series.
