Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tropical Mirror   We describe the tropical curves in projective space and define the tropical
Gromov-Witten invariants. We introduce amplitudes for the higher topological
quantum mechanics with circle action on graphs and show that the amplitudes are
equal to the tropical Gromov-Witten invariants. The state-operator
correspondence in topological quantum mechanics on graphs allows to express the
sum of the amplitudes in A-type quantum mechanics as the amplitude in deformed
quantum mechanics, naturally identified as the B-type quantum mechanics. We use
the equality between the amplitudes for three observables to prove the mirror
symmetry for cohomology rings.

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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph