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arXiv · 1811.06811

An infinite-dimensional index theorem and the Higson-Kasparov-Trout algebra

Doman Takata
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Abstract

We have been studying the index theory for some special infinite-dimensional manifolds with a "proper cocompact" actions of the loop group LT of the circle T, from the viewpoint of the noncommutative geometry. In this paper, we will introduce the LT-equivariant KK-theory and we will construct three KK-elements: the index element, the Clifford symbol element and the Dirac element. These elements satisfy a certain relation, which should be called the (KK-theoretical) index theorem, or the KK-theoretical Poincar\'e duality for infinite-dimensional manifolds. We will also discuss the assembly maps.

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Doman Takata. 2018-11-16. An infinite-dimensional index theorem and the Higson-Kasparov-Trout algebra. https://doi.org/10.2140/akt.2022.7.1

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