Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformations of circle-valued Morse functions on surfaces   Let $M$ be a smooth connected orientable compact surface. Denote by
$F(M,S^1)$ the space of all Morse functions $f:M\to S^1$ having no critical
points on the boundary of $M$ and such that for every boundary component $V$ of
$M$ the restriction $f|_{V}:V\to S^1$ is either a constant map or a covering
map. Endow $F(M,S^1)$ with the $C^{\infty}$-topology. In this note the
connected components of $F(M,S^1)$ are classified. This result extends the
results of S. V. Matveev, V. V. Sharko, and the author for the case of Morse
functions being locally constant on the boundary of $M$.

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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an