Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spin structures on loop spaces that characterize string manifolds   Classically, a spin structure on the loop space of a manifold is a lift of
the structure group of the looped frame bundle from the loop group to its
universal central extension. Heuristically, the loop space of a manifold is
spin if and only if the manifold itself is a string manifold, against which it
is well-known that only the if-part is true in general. In this article we
develop a new version of spin structures on loop spaces that exists if and only
if the manifold is string, as desired. This new version consists of a classical
spin structure plus a certain fusion product related to loops of frames in the
manifold. We use the lifting gerbe theory of Carey-Murray, recent results of
Stolz-Teichner on loop spaces, and some own results about string geometry and
Brylinski-McLaughlin transgression.

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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph