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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