Abstract
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 specify an “appropriate form” of the index theorem to formulate a loop space version, we formulate and prove an equivariant index theorem for non-compact S1-manifolds with a compact fixed-point set. In order to formulate it, we use a ring of formal power series.
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