Strong positivity for the skein algebras of the -punctured sphere and of the -punctured torus
arXiv:2009.02266 · doi:10.1007/s00220-022-04512-9
Abstract
The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the character variety of a topological surface. We realize the skein algebra of the -punctured sphere as the output of a mirror symmetry construction based on higher genus Gromov-Witten theory and applied to a complex cubic surface. Using this result, we prove the positivity of the structure constants of the bracelets basis for the skein algebras of the -punctured sphere and of the -punctured torus. This connection between topology of the -punctured sphere and enumerative geometry of curves in cubic surfaces is a mathematical manifestation of the existence of dual descriptions in string/M-theory for the gauge theory.
arXiv comment59 pages, 17 figures. Final version published in Communications in Mathematical Physics
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