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The localized Fourier-Laplace transform of the Gau{\ss}-Manin system of$f\colon \mathbb{G}_m \to \mathbb{A}^1,\ x \mapsto x + x^{-3}$ is a$\mathcal{D}_{\mathbb{G}_m}$-module, having a regular singularity at $0$ and anirregular one at $\infty$. By mirror symmetry, it is closely related to thequantum connection of the weighted projective line $\mathbb{P}(1,3)$. Followingresults of A. D'Agnolo, M. Hien, G. Morando and C. Sabbah from 2017, we computeits Stokes multipliers at $\infty$ by purely topological methods. We compare itto the Gram matrix of the Euler-Poincar\'{e} pairing on$D^b(\text{Coh}(\mathbb{P}(1,3)))$.

Topological computation of the Stokes matrices of the weighted projective line $\mathbb{P}(1,3)$