Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The space of short ropes and the classifying space of the space of long
  knots   We prove affirmatively the conjecture raised by J. Mostovoy; the space of
short ropes is weakly homotopy equivalent to the classifying space of the
topological monoid (or category) of long knots in $\mathbb{R}^3$. We make use
of techniques developed by S. Galatius and O. Randal-Williams to construct a
manifold space model of the classifying space of the space of long knots, and
we give an explicit map from the space of short ropes to the model in a
geometric way.

24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph