Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Augmentations and Rulings of Legendrian Knots   For any Legendrian knot in (R^3,ker(dz-ydx)), we show that the existence of
an augmentation to any field of the Chekanov-Eliashberg differential graded
algebra over Z[t,t^{-1}] is equivalent to the existence of a ruling of the
front diagram, generalizing results of Fuchs, Ishkhanov, and Sabloff. We also
show that any even graded augmentation must send t to -1.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin