Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kauffman-Jones polynomial of a curve on a surface   We introduce a Kauffman-Jones type polynomial $\mathcal{L}_{\gamma}(A)$ for a
curve $\gamma$ on an oriented surface, whose endpoints are on the boundary of
the surface. The polynomial $\mathcal{L}_{\gamma}(A)$ is a Laurent polynomial
in one variable $A$ and is an invariant of the homotopy class of $\gamma$. As
an application, we obtain an estimate in terms of the span of
$\mathcal{L}_{\gamma}(A)$ for the minimum self-intersection number of a curve
within its homotopy class. We then give a chord diagrammatic description of
$\mathcal{L}_{\gamma}(A)$ and show some computational results on the span of
$\mathcal{L}_{\gamma}(A)$.

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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga