We construct a Frobenius structure whose intersection form coincides with the generalized Cartan matrix of the ℓ-Kronecker quiver K ℓ and underlying complex manifold is isomorphic to the space of stability conditions for the bounded derived category of finitely generated modules over the path algebra CK ℓ .
The notion of the Gamma integral structure for the quantum cohomology of an algebraic variety was introduced by Iritani, Katzarkov-Kontsevich-Pantev. In this paper, we define the Gamma integral structure for an invertible polynomial of chain type. Based on the Γ-conjecture by Iritani, we prove that the Gamma integral structure is identified with the natural integral structure for the Berglund-Hübsch transposed polynomial by the mirror isomorphism.
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