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

Doman Takata  (Tokyo University)

10:00-11:00, August 4, 2020   Zoom 514 693 6752

Abstract:

The overall goal of my research is to formulate an index theory for infinite-dimensional manifolds in the language of KK-theory. As a first step, I have been studying the case of a manifold with a proper cocompact LS^1-action, where LS^1 is the loop group of the circle. Although this project has not been completed, I have established large part of the theory. In this talk, I will outline my newest paper (arXiv:2007.08899), and then I will explain the construction of the `index element'. In this construction, I will consider the C^*-algebra of a Hilbert space defined by Higson, Kasparov and Trout, which can be interesting for people in other areas.

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