Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loops of Legendrians in contact 3-manifolds   We study homotopically non-trivial spheres of Legendrians in the standard
contact R3 and S3. We prove that there is a homotopy injection of the
contactomorphism group of S3 into some connected components of the space of
Legendrians induced by the natural action. We also provide examples of loops of
Legendrians that are non-trivial in the space of formal Legendrians, and thus
non-trivial as loops of Legendrians, but which are trivial as loops of smooth
embeddings for all the smooth knot types.

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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th