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arXiv · 2402.10867

On the quantum differential equations for a family of non-K\"ahler monotone symplectic manifolds

Kai Hugtenburg
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Abstract

In this paper we prove Gamma Conjecture $1$ for twistor bundles of hyperbolic $6$ manifolds, which are monotone symplectic manifolds which admit no K\"ahler structure. The proof involves a direct computation of the $J$-function, and a version of Laplace's method for estimating power series (as opposed to integrals). This method allows us to rephrase Gamma Conjecture $1$ in certain situations to an Ap\'ery-like discrete limit. We use this to give a simple proof of Gamma Conjecture $1$ for projective spaces. Additionally we show that the quantum connections of the twistor bundles we consider have unramified exponential type.

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Kai Hugtenburg. 2024-02-16. On the quantum differential equations for a family of non-K\"ahler monotone symplectic manifolds. https://arxiv.org/abs/2402.10867

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