Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Skeins on Branes   We give a geometric interpretation of the coefficients of the HOMFLYPT
polynomial of any link in the three-sphere as counts of holomorphic curves. The
curves counted live in the resolved conifold where they have boundary on a
shifted copy of the link conormal, as predicted by Ooguri and Vafa.. To prove
this, we introduce a new method to define invariant counts of holomorphic
curves with Lagrangian boundary: we show geometrically that the wall crossing
associated to boundary bubbling is the framed skein relation. It then follows
that counting holomorphic curves by the class of their boundary in the skein of
the Lagrangian brane gives a deformation invariant curve count. This is a
mathematically rigorous incarnation of the fact that boundaries of open
topological strings create line defects in Chern-Simons theory, as described by
Witten.
  The technical key to skein invariance is a new compactness result: if the
Gromov limit of J-holomorphic immersions collapses a curve component, then its
image has a singularity worse than a node.

29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph