Gamma conjecture II for quadrics

摘要: The Gamma conjecture II for the quantum cohomology of a Fano manifold $F$, proposed by Galkin, Golyshev and Iritani, describes asymptotic behavior flat sections Dubrovin connection near irregular singularities, in terms full exceptional collection, if there exists, $\mathcal D^b(F)$ $\widehat{\Gamma}$-integral structure. In this paper, smooth quadric hypersurfaces we prove convergence II. For proof, first give criterion on manifolds with semisimple cohomology, Dubrovin's theorem analytic continuations Frobenius manifolds. Then work out closed formula Chern characters spinor bundles quadrics. By deformation-invariance Gromov-Witten invariants show that can be reconstructed its ambient part, use to obtain estimations. Finally complete proof quadrics explicit expansions corresponding Kapranov's collections an application our criterion.