Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The tropological vertex   The theory of the topological vertex was originally proposed by Aganagic,
Klemm, Mari\~no and Vafa as a means to calculate open Gromov-Witten invariants
of toric Calabi-Yau threefolds. In this paper, we place the topological vertex
within the context of relative Gromov-Witten invariants of log Calabi-Yau
manifolds and describe how these invariants can be effectively computed via a
gluing formula for the enumeration of tropical curves in a singular integral
affine space. This richer context allows us to prove that the topological
vertex possesses certain tropical symmetries. These symmetries are captured by
the action of a quantum torus Lie algebra that is related to a quantisation of
the Lie algebra of the tropical vertex group of Gross, Pandharipande and
Siebert. Finally, we demonstrate how this algebra of symmetries leads to an
explicit description of the topological vertex and related Gromov-Witten
invariants.

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The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg