Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loop homology algebra of a closed manifold   The loop homology of a closed orientable manifold $M$ of dimension $d$ is the
ordinary homology of the free loop space $M^{S^1}$ with degrees shifted by $d$,
i.e. $\mathbb H_*(M^{S^1}) = H_{*+d}(M^{S^1})$. Chas and Sullivan have defined
a loop product on $\mathbb H_*(M^{S^1})$ and an intersection morphism $I :
\mathbb H_*(M^{S^1}) \to H_*(\Omega M)$. The algebra $\mathbb H_*(M^{S^1})$ is
commutative and $I$ is a morphism of algebras. In this paper we produce a model
that computes the algebra $\mathbb H_*(M^{S^1})$ and the morphism $I$. We show
that the kernel of $I$ is nilpotent and that the image is contained in the
center of $H_*(\Omega M)$, which is in general quite small.

3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
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The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph