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Tau Functions from Joyce Structures
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We argued in [Proc. Sympos. Pure Math., Vol. 103, American Mathematical Society, Providence, RI, 2021, 1–66, arXiv:1912.06504] that, when a certain sub-exponential growth property holds, the Donaldson–Thomas invariants of a 3-Calabi–Yau triangulated category should give rise to a geometric structure on its space of stability conditions called a Joyce structure. In this paper, we show how to use a Joyce structure to define a generating function which we call the $\tau$-function. When applied to the derived category of the resolved conifold, this reproduces the non-perturbative topological string partition function of [J. Differential Geom. 115 (2020), 395–435, arXiv:1703.02776]. In the case of the derived category of the Ginzburg algebra of the A$_2$ quiver, we obtain the Painlevé I $\tau$-function.
Keywords: Donaldson–Thomas invariants, topological string theory, hyperkähler geometry, twistor spaces
Mots-clés : Painlevé equations. 
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     author = {Tom Bridgeland},
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Tom Bridgeland. Tau Functions from Joyce Structures. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a111/

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