Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Aspects of the Equivariant Index Theory of
  Infinite-Dimensional LT-Manifolds   Let $T$ be the circle group and let $LT$ be its loop group. We formulate and
investigate several topological aspects of the $LT$-equivariant index theory
for proper $LT$-spaces, where proper $LT$-spaces are infinite-dimensional
manifolds equipped with "proper cocompact" $LT$-actions. Concretely, we
introduce "$\mathcal{R}KK$-theory for infinite-dimensional manifolds", and by
using it, we formulate an infinite-dimensional version of the $KK$-theoretical
Poincar\'e duality homomorphism, and an infinite-dimensional version of the
$\mathcal{R}KK$-theory counterpart of the assembly map, for proper $LT$-spaces.
  The left hand side of the Poincar\'e duality homomorphism is formulated by
the "$C^*$-algebra of a Hilbert manifold" introduced by Guoliang Yu. Thus, the
result of this paper suggests that this construction carries some topological
information of Hilbert manifolds. In order to formulate the assembly map in a
classical way, we need crossed products, which require an invariant measure of
a group. However, there is an alternative formula to define them using
generalized fixed-point algebras. We will adopt it as the definition of
"crossed products by $LT$".

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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph